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# T. Yuda's research while affiliated with The University of Tokyo and other places

## Publications (289)

Article
Full-text available
The CALorimetric Electron Telescope (CALET), launched for installation on the International Space Station (ISS) in August, 2015, has been accumulating scientific data since October, 2015. CALET is intended to perform long-duration observations of high-energy cosmic rays onboard the ISS. CALET directly measures the cosmic-ray electron spectrum in th...
Article
We analyze the Sun’s shadow observed with the Tibet-III air shower array and find that the shadow’s center deviates northward (southward) from the optical solar disk center in the “away” (“toward”) interplanetary magnetic field (IMF) sector. By comparing with numerical simulations based on the solar magnetic field model, we find that the average IM...
Article
Full-text available
First results of a cosmic-ray electron and positron spectrum from 10 GeV to 3 TeV is presented based upon observations with the CALET instrument on the International Space Station starting in October, 2015. Nearly a half million electron and positron events are included in the analysis. CALET is an all-calorimetric instrument with total vertical th...
Article
Full-text available
In August 2015, the CALorimetric Electron Telescope (CALET), designed for long exposure observations of high energy cosmic rays, docked with the International Space Station (ISS) and shortly thereafter began to collect data. CALET will measure the cosmic ray electron spectrum over the energy range of 1 GeV to 20 TeV with a very high resolution of 2...
Article
We report on the analysis of the 10-1000 TeV large-scale sidereal anisotropy of Galactic cosmic rays (GCRs) with the data collected by the Tibet Air Shower Array from 1995 October to 2010 February. In this analysis, we improve the energy estimate and extend the decl. range down to -30°. We find that the anisotropy maps above 100 TeV are distinct fr...
Article
We present upper limits in the hard X-ray and gamma-ray bands at the time of the LIGO gravitational-wave event GW 151226 derived from the CALorimetric Electron Telescope (CALET) observation. The main instrument of CALET, CALorimeter (CAL), observes gamma-rays from ~1 GeV up to 10 TeV with a field of view of ~2 sr. The CALET gamma-ray burst monitor...
Article
A 100 m2 muon detector (MD) was successfully constructed under the existing Tibet air shower (AS) array in the late fall of 2007. The sensitivity of the Tibet AS array to cosmic gamma rays can be improved by selecting muon-poor events with the MD. Our MC simulation of the MD response reasonably agrees with the experimental data in terms of the char...
Data
Full-text available
Article
Full-text available
The CALorimetric Electron Telescope (CALET) is a space experiment, currently under development by Japan in collaboration with Italy and the United States, which will measure the flux of cosmic-ray electrons (and positrons) up to 20 TeV energy, of gamma rays up to 10 TeV, of nuclei with Z from 1 to 40 up to 1 PeV energy, and will detect gamma-ray bu...
Article
Full-text available
The CALorimetric Electron Telescope (CALET) is a space experiment, currently under development by Japan in collaboration with Italy and the United States, which will measure the flux of cosmic-ray electrons (and positrons) up to 20 TeV energy, of gamma rays up to 10 TeV, of nuclei with Z from 1 to 40 up to 1 PeV energy, and will detect gamma-ray bu...
Article
The CALorimetric Electron Telescope (CALET) is a space experiment, currently under development by Japan in collaboration with Italy and the United States, which will measure the flux of cosmic-ray electrons (and positrons) up to 20 TeV energy, of gamma rays up to 10 TeV, of nuclei with Z from 1 to 40 up to 1 PeV energy, and will detect gamma-ray bu...
Article
The CALorimetric Electron Telescope (CALET) space experiment, currently under development by Japan in collaboration with Italy and the United States, will measure the flux of cosmic-ray electrons (including positrons) to 20 TeV, gamma rays to 10 TeV and nuclei with Z=1 to 40 up to 1,000 TeV during a two-year mission on the International Space Stati...
Article
We report on a clear solar-cycle variation of the Sun's shadow in the 10 TeV cosmic-ray flux observed by the Tibet air shower array during a full solar cycle from 1996 to 2009. In order to clarify the physical implications of the observed solar cycle variation, we develop numerical simulations of the Sun's shadow, using the Potential Field Source S...
Article
In this paper, we report solar neutron events detected in the solar cycle 23, especially three interesting events detected on November 23rd and 28th 1998 in Tibet and October 28th 2003 in Tsumeb.
Article
Using the Tibet-III air shower array, we search for steady TeV γ-rays from 18 pulsars in the Fermi Large Area Telescope pulsar catalog. Among them, we observe 8 sources including the Crab instead of the expected 0.41 sources at a significance of 2 σ or more excess. Under the assumption of Poisson distribution, the chance probability is estimated to...
Article
The Tibet AS-gamma collaboration is constructing 4500 m2 underground muon detector array by using water Cherenkov technique, to form the TIBET AS+MD hybrid array. The muon detector will improve the sensitivity of gamma ray and electron observation above 10 TeV by rejecting the cosmic ray background. In TIBET AS+MD, both water-recycling system and c...
Article
The galactic cosmic-ray anisotropy at TeV energies has a large-scale deficit region distributed around 150 to 240 degrees in right ascension, which is called "Loss-Cone". The Milagro experiment in the U.S. detected a significant increase in the Loss-Cone amplitude at 6 TeV from July 2000 to July 2007, and argued that it could be due to variations i...
Article
We have operated the 500 m2 Yangbajing air-shower core (YAC-II) detector array near the center of the Tibet air-shower array ( Tibet-III ) to study the cosmic-ray chemical composition at the knee energy region since August, 2011. YAC-II array consists of 124 YAC detector units. Each unit of YAC-II consists of a lead layer of 3.5 cm thick and a scin...
Article
A possible origin of the large-scale anisotropy of TeV galactic cosmic rays is discussed. It can be well modeled by a superposition of the Global Anisotropy and the Midscale Anisotropy. The Global Anisotropy would be generated by galactic cosmic rays interacting with the magnetic field in the local interstellar space of a few parsec scale surroundi...
Article
New air-shower core detector YAC has been developed to measure cosmic-ray mass composition around the energy region of the knee. Prototype experiment YAC1 was successfully carried out in 2009-2010 together with Tibet III air-shower array. Enlarged installation YAC2 is also under construction and will be operated in fall 2011. Preliminary result of...
Article
Aiming at the observation of cosmic-ray chemical composition at the knee energy region, a new type airshower- core detector (YAC, Yangbajing Air shower Core array) has been developed and set up at Yangbajing, 4300 m a.s.l. in Tibet, China since August, 1st, 2011. YAC will work together with the Tibet-III array and a large muon detector as a hybrid...
Article
A hybrid experiment has been started by ASγ collaboration at Tibet, China, since May 2009, that consists of a burst-detector-grid (YAC, Yangbajing Air shower Core array) and the Tibet air-shower array (Tibet-III). The first step of YAC, called YAC-I, contains 16 detector units and observes high energy electromagnetic particles in air-shower cores w...
Article
We are now operating the 500 m2 Yangbajing air-shower core (YAC-II) array near the center of the Tibet air-shower array ( Tibet-III ) to observe cosmic-ray chemical composition at the knee energy region since February 2011. The first step of YAC, called YAC-I, containing 16 detector units, was operated from May, 2009 to February, 2010. In this pape...
Article
We analyze the solar cycle variation of the Sun's shadow in 10 TeV cosmic ray intensity observed with the Tibet air shower array over an entire period of the Solar Cycle 23 between 1996 and 2008. The amplitude of the variation is as large as one half of the deficit intensity expected when all cosmic rays arriving from the direction of the optical S...
Article
There are various explanations about the origin of lightning during thunderstorms. A possible explanation is that the cosmic rays may be caused of triggers of lightning. In order to measure any correlations between atmospheric charged particles and atmospheric electric field, we have installed some atmospheric electric field meter inside the Tibet...
Article
A new hybrid experiment has been started by ASγ experiment at Tibet, China, since August 2011, which consists of a low threshold burst-detector-grid (YAC-II, Yangbajing Air shower Core array), the Tibet air-shower array (Tibet-III) and a large underground water Cherenkov muon detector (MD). In this paper, the capability of the measurement of the ch...
Article
We are now proposing the 10,000m2 water-Cherenkov-type muon detector (MD) array under the Tibet air shower (AS) array to find new gamma-ray sources with a wide field of view and unprecedented flux sensitivity. In the late fall of 2007, a prototype MD in area of 100m2 was constructed under the existing Tibet AS array. In this paper, we search for su...
Article
We plan to build a large (approximately 10,000 m2) water-Cherenkov-type muon detector array under the existing Tibet air shower array at 4,300 m above sea level, to observe 10-1000 TeV gamma rays from cosmic-ray accelerators in our Galaxy with wide field of view at very low background level. The gamma-ray induced air shower has significantly less m...
Article
The energy spectrum of cosmic rays around the knee measured by Tibet air-shower experiment is summarized and its characteristic features are discussed under two possible scenarios. The result of Tibet experiment measured over wide range of 1014-1017 eV with high statistics provided details of the knee at the energy around 4×1015 eV. The study of th...
Article
Full-text available
We analyze the large-scale two-dimensional sidereal anisotropy of multi-TeV cosmic rays by Tibet Air Shower Array, with the data taken from 1999 November to 2008 December. To explore temporal variations of the anisotropy, the data set is divided into nine intervals, each in a time span of about one year. The sidereal anisotropy of magnitude about 0...
Article
Full-text available
Using the Tibet-III air shower array, we search for TeV gamma-rays from 27 potential Galactic sources in the early list of bright sources obtained by the Fermi Large Area Telescope at energies above 100 MeV. Among them, we observe 7 sources instead of the expected 0.61 sources at a significance of 2 sigma or more excess. The chance probability from...
Article
Full-text available
We develop a model anisotropy best-fitting to the two-dimensional sky-map of multi-TeV galactic cosmic ray (GCR) intensity observed with the Tibet III air shower (AS) array. By incorporating a pair of intensity excesses in the hydrogen deflection plane (HDP) suggested by Gurnett et al., together with the uni-directional and bi-directional flows for...
Article
Full-text available
The Tibet-III air shower array, consisting of 533 scintillation detectors, has been operating successfully at Yangbajing in Tibet, China since 1999. Using the data set collected by this array from 1999 November through 2005 November, we obtained the energy spectrum of γ-rays from the Crab Nebula, expressed by a power law as (dJ/dE) = (2.09 ± 0.32)...
Article
Full-text available
We report the observations of TeV gamma-ray flares from Markarian 501 using the Telescope Array Prototype. The observations were carried out continuously from the end of March to the end of July of 1997. The energy spectrum and the time variation of the gamma-ray intensities are shown. The intensity has been changed by an order of magnitude in this...
Article
The Tibet-III air shower array, consisting of 789 scintillation detectors, has been operating successfully at Yangbajing in Tibet since 1999. Some recent results on gamma-ray observation by the Tibet-III air shower array are introduced and its future prospects of gamma-ray observation will be discussed.
Article
Recent results and future prospects of the Tibet air-shower experiment are reported on the all-particle energy spectrum and the chemical composition of cosmic rays around 1015eV energy range. The knee of the all-particle energy spectrum has been clearly observed at the energy around 4x1015eV by Tibet III air-shower array located at Yangbajing, Tibe...
Article
The Tibet-III air shower array, consisting of 789 scintillation detectors, has been operating successfully at Yangbajing in Tibet since 1999. Some recent results on gamma-ray observation by the Tibet-III air shower array are introduced and its future prospects of gamma-ray observation will be discussed.
Article
A network of solar neutron telescopes has been developed since the middle of solar cycle 22. We have detected several important solar neutron events until the end of solar cycle 23 using solar neutron telescopes, but the accumulation of more solar neutron events is indispensable to eclucidate the acceleration mechanism of high energy particles. The...
Article
We have analyzed the large scale sidereal anisotropy of multi-TeV Galactic cosmic rays by Tibet Air Shower Array, with the data taken from Nov. 1999 to Nov. 2005. To study the temporal variation of the anisotropy, the data set is divided into 6 samples, each in a time scale of one year.It is shown that the sidereal anisotropy with the magnitude abo...
Article
The solar activity is gradually changing from the Solar Cycle 23 to 24. Sun's shadow generated by multi-TeV cosmic-ray particles has been continuously observed with the Tibet-II and Tibet- III air shower array in 1996 through 2008. We have shown that the Sun's shadow is strongly affected by the solar and interplanetary magnetic fields changing with...
Article
We carried out electron observations with balloons to investigate acceleration and propagation of electrons in the universe. We developed BETS (Balloon-borne Electron Telescope with Scintillation fibers) for electron observations in Sanriku. We obtained electron energy spectrum from 10 GeV to 100 GeV with it. At higher energies, the energy spectrum...
Article
Results of a steady TeV γ-ray point-source search using data taken from the Tibet HD (1997 February-1999 September) and Tibet III (1999 November-2001 October) arrays are presented. From 0° to 60° in declination, significant excesses from the well-known steady source Crab Nebula and the high state of the flare-type source Markarian 421 are observed....
Article
Full-text available
We searched for steady PeV gamma-ray emission from the Monogem ring region with the Tibet air shower array from 1997 February to 2004 October. No evidence for statistically significant gamma-ray signals was found in a region 111° ≤ R.A. < 114°, 125 ≤ decl. < 155 in the Monogem ring where the MAKET-ANI experiment recently claimed a positive detectio...
Article
Several strong TeV γ-ray flares were detected from Mrk 421 in the years 2000 and 2001 by the Tibet III air shower array at a level of statistical significance of 5.1 σ. Mrk 421 was unprecedentedly active at X-ray and TeV γ-ray energies during this period, and a positive correlation was found between the change of the all-sky monitor Rossi X-Ray Tim...
Article
Cosmic-ray electrons have been observed in the energy region from 10 GeV to 1 TeV with the PPB-BETS by a long duration balloon flight using a Polar Patrol Balloon (PPB) in Antarctica. The observation was carried out for 13 days at an average altitude of 35 km in January 2004. The PPB-BETS detector is an imaging calorimeter composed of scintillating...
Article
Full-text available
We have observed cosmic-ray electrons from 10 GeV to 800 GeV by a long duration balloon flight using Polar Patrol Balloon (PPB) in Antarctica. The observation was carried out for 13 days at an average altitude of 35 km in January 2004. The detector is an imaging calorimeter composed of scintillating-fiber belts and plastic scintillators inserted be...
Article
The Tibet air shower array, which has an effective area of 36,900 m2, has been in operation at Yangbajing in Tibet, China at an altitude of 4,300 m above sea level. In this paper, we will briefly introduce the recent gamma-ray observation with the present Tibet air shower array and our future plan which is called the Tibet muon detector (MD) projec...
Article
We present an updated all-particle energy spectrum of primary cosmic rays in a wide range from 10(14) to 10(17) eV using 5.5 x 107 events collected from 2000 November through 2004 October by the Tibet-III air-shower array located 4300 m above sea level (an atmospheric depth of 606 g cm(-2)). The size spectrum exhibits a sharp knee at a correspondin...
Article
The CALorimetric Electron Telescope, CALET, is a new Space Observatory being developed for the Japanese Experiment Module Exposed Facility, JEM-EF, of the International Space Station. Major scientific objectives are to search for nearby cosmic ray sources and dark matter by carrying out a precise measurement of the electron spectrum from 10's of Ge...
Article
The CALorimetric Electron Telescope, CALET, mission is proposed for the Japanese Experiment Module Exposed Facility, JEM-EF, of the International Space Station. The scientific objective is to investigate the origin of the cosmic electrons and gamma-rays in very high energy region. The detector is composed of an imaging calorimeter of scintillating...
Article
We report on the spectral index of cosmic rays around 10 TeV energy region obtained by observation of the Compton-Getting anisotropy due to the terrestrial orbital motion around the Sun with the Tibet III air shower array during the period from 1999 to 2005. The spectral index has turned out to be 2.99±0.54, which is consistent with 2.74 by the dir...
Article
We searched for steady 100 TeV gamma-ray point sources from -10° to +70° in declination based on six year data obtained from Nov. 1999 to Nov. 2005 by the Tibet air shower array. No new source was found and no significant excess of events could be detected from known TeV sources. We set flux upper limits above 100 TeV on several nearby objects loca...
Article
Full-text available
The Tibet air shower array, which has an effective area of 37,000 square meters and is located at 4300 m in altitude, has been observing air showers induced by cosmic rays with energies above a few TeV. We have a plan to add a large muon detector array to it for the purpose of increasing its sensitivity to cosmic gamma rays in the 100 TeV energy re...
Article
Full-text available
The Tibet air shower array, which has an effective area of 37,000 square meters and is located at 4300 m in altitude, has been observing air showers induced by cosmic rays with energies above a few TeV. We are planning to add a large muon detector array to it for the purpose of increasing its sensitivity to cosmic gamma rays in the 100 TeV (10 - 10...
Article
Full-text available
The amplitude of the Compton-Getting (CG) anisotropy contains the power-law index of the cosmic-ray energy spectrum. Based on this relation and using the Tibet air-shower array data, we measure the cosmic-ray spectral index to be $-3.03 \pm 0.55_{stat} \pm < 0.62_{syst}$ between 6 TeV and 40 TeV, consistent with $-$2.7 from direct energy spectrum m...
Article
We have observed the shadowing of galactic cosmic ray flux in the direction of the moon, the so-called moon shadow, using the Tibet-III air shower array operating at Yangbajing (4300 m a.s.l.) in Tibet since 1999. Almost all cosmic rays are positively charged; for that reason, they are bent by the geomagnetic field, thereby shifting the moon shadow...
Article
A new solar neutron telescope has been constructed at Yangbajing, Tibet (600 g/cm2) and has been successfully operated for 8 years. During this time several interesting events were observed in coincidence with large solar flares. In this paper the authors discuss a directional count rate enhancement 1998 November 28 as to whether it is related to s...
Article
We show that the large‐scale anisotropy of ∼5 TeV galactic cosmic ray (GCR) intensity observed by Tibet Air Shower experiment can be reproduced by the superposition of a bi‐directional and uni‐directional flows (UDF and BDF) of GCRs. The heliosphere is located inside the local interstellar cloud (LIC) very close to the inner edge of the LIC. If th...
Article
Gigantic solar flares exceeding X-class occurred 10 times in September, 2005, and 4 times in December, 2006, although the Sun had already been in the declining phase in solar cycle 23. In this paper, we report on results of the search for solar neutron events associated with these 14 X-class flares, using data obtained by the international network...
Article
We have observed cosmic-ray electrons from 10 GeV to 1 TeV with PPB-BETS by a long duration balloon flight using Polar Patrol Balloon (PPB) in Antarctica. The observation was carried out for 13 days at an altitude of 35 km in January 2004. The detector is an imaging calorimeter composed of scintillating-fiber belts and plastic scintillators inserte...
Article
Full-text available
We are developing the CALorimetric Electron Telescope, CALET, mission for the Japanese Experiment Module Exposed Facility, JEM-EF, of the International Space Station. Major scientific objectives are to search for the nearby cosmic ray sources and dark matter by carrying out a precise measurement of the electrons in 1 GeV - 10 TeV and rays in 20 MeV...
Article
We have observed cosmic-ray electrons from 10 to 1000 GeV by a long duration balloon flight using Polar Patrol Balloon (PPB) in Antarctica. The observation was carried out for 13 days at an altitude of 35 km in January 2004. The detector is an imaging calorimeter composed of scintillating-fiber belts and plastic scintillators inserted between lead...
Article
Simultaneous observation of γ-families and their accompanying air showers was performed at Yangbajing (4300 m above sea level) in Tibet with the emulsion chambers and burst detectors which were linked with the Tibet-II air-shower array. For three years operation, we observed 177 γ-families (∑Eγ > 20 TeV) accompanying air showers with the size Ne >...
Article
According to many solar observations, the solar activity, during the Solar Cycle 23, is gradually declining to the quiet phase from the high state in 2000–2004. The Tibet air shower array has been continuing the observation of the shadow that cosmic rays make in the 0273-1177/\$30 Ó direction of the sun or the moon since 1991. We have shown the infl...
Article
The intensity of Galactic cosmic rays is nearly isotropic because of the influence of magnetic fields in the Milky Way. Here, we present two-dimensional high-precision anisotropy measurement for energies from a few to several hundred teraelectronvolts (TeV), using the large data sample of the Tibet Air Shower Arrays. Besides revealing finer details...
Article
Full-text available
The Tibet hybrid experiment composed of emulsion chambers, burst detectors and the Tibet-II air-shower array was done at Yangbajing (4,300m above sea level, 606 g/cm2) in Tibet. For 3-year operation, we have observed 177 gamma-families (SigmaEgamma > 20 TeV) accompanying air showers with the shower size Ne > 2 × 105. Using this data set and a neura...
Chapter
The Long-Term variation of the solar diurnal anisotropy of the galactic cosmic ray intensity in the Sub-TeV region is studied by using data recorded over 20 years with the deep underground muon detector at Matsushiro in Japan since 1984. The harmonic dial of the diurnal variation shows a clear 11-Year change. At around 1987 and 1998, the variation...
Article
We obtained new upper limits on the diffuse gamma rays from the inner Galactic (IG) and outer Galactic (OG) planes in 3–10 TeV region, using the Tibet air shower data and new Monte Carlo simulation results. A difference of the effective area of the air-shower array for observing gamma rays and cosmic rays was carefully taken into account in this an...
Article
A hybrid experiment consisting of emulsion chambers, burst detectors and the Tibet-II air-shower array was carried out at Yangbajing (4300 m a.s.l., 606 g/cm2) in Tibet to obtain the energy spectra of primary protons and heliums. From three-year operation, these energy spectra are deduced between 10 15 and 1016 eV by triggering the air showers asso...
Article
Full-text available
In this paper, we report solar neutron events detected in the solar cycle 23, especially three interesting events detected on November 23rd and 28th 1998 in Tibet and October 28th 2003 in Tsumeb.


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Definition of: x (1) (eXit) To exit, close or delete. See X button.
(2) (heX) In programming, a symbol used to identify a hexadecimal number. For example, "0x0A" and "\x0A" specify the hex number 0A. See also X Window and MDI-X port.
(3) (times the original) A performance rating for optical drives, based on rotation speed (RPM) of the platter. Each "x" means "times the speed of the first specification," thus 10x means 10 times as fast as the original drive. See CD-ROM drives and DVD drives.
(4) (x-) The prefix used to describe a MIME type. For example, x-pdf and x-gzip refer to PDF and Gnu ZIP file formats, respectively. See MIME type.
(5) A prefix for cross; for example, x-platform means "cross-platform." See cross platform.
(6) (Mac OS X) X is the Roman Numeral for 10; thus OS X means "OS 10." See Mac OS X.
(7) (eXperience) See UX designer and user experience.

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# The essential norm of a composition operator

### Abstract

We express the essential norm of a composition operator on the Hardy space $H^2$ as the asymptotic upper bound of a quantity involving the Nevanlinna counting function of the inducing map. There results a complete function theoretic characterization of the compact composition operators on $H^2$. Simlar results holds for the weighted Bergman spaces of the unit disc. As consequences we obtain:

(i) estimates of the essential norm of a composition operator in terms of the angular derivative of its inducing map;

(ii) a new proof of a recently obtained characterization of the compact composition operators on the weighted Bergman spaces; and

(iii) a new proof of a peak set theorem for holomorphic Lipschitz functions.

Joel H. Shapiro


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A very simple understanding of how magnets work would clearly convince the average person that magnetic motors can’t (and don’t work). Pray tell where does the energy come from? The classic response is magnetic energy from when they were made. Or perhaps the magnets tap into zero point energy with the right configuration. What about they harness the earth’s gravitational field. Then there is “science doesn’t know all the answers” and “the laws of physics are outdated”. The list goes on with equally implausible rubbish. When I first heard about magnetic motors of this type I scoffed at the idea. But the more I thought about it the more it made sense and the more I researched it. Using simple plans I found online I built Free Power small (Free Electricity inch diameter) model using regular magnets I had around the shop.
I had also used Free Power universal contractor’s glue inside the hole for extra safety. You don’t need to worry about this on the outside sections. Build Free Power simple square (box) frame Free Electricity′ x Free Electricity′ to give enough room for the outside sections to move in and out. The “depth” or length of it will depend on how many wheels you have in it. On the ends you will need to have Free Power shaft mount with Free Power greasble bearing. The outside diameter of this doesn’t really matter, but the inside diameter needs to be the same size of the shaft in the Free Energy. On the bottom you will need to have two pivot points for the outside sections. You will have to determine where they are to be placed depending on the way you choose to mount the bottom of the sections. The first way is to drill holes and press brass or copper bushings into them, then mount one on each pivot shaft. (That is what I did and it worked well.) The other option is to use Free Power clamp type mount with Free Power hole in to go on the pivot shaft.
Free Energy to leave possible sources of motive force out of it. 0. 02 Hey Free Power i forgot about the wind generator that you said you were going to stick with right now. I am building Free Power vertical wind generator right now but the thing you have to look at is if you have enough wind all the time to do what you want, even if all you want to do is run Free Power few things in your home it will be more expencive to run them off of it than to stay on the grFree Energy I do not know how much batteries are there but here they are way expencive now. Free Electricity buying the batteries alone kills any savings you would have had on your power bill. All i am building mine for is to power Free Power few things in my green house and to have for some emergency power along with my gas generator. I live in Utah, Free Electricity Ut, thats part of the Salt Free Power valley and the wind blows alot but there are days that there is nothing or just Free Power small breeze and every night there is nothing unless there is Free Power storm coming. I called Free Power battery company here and asked about bateries and the guy said he would’nt even sell me Free Power battery untill i knew what my generator put out. I was looking into forklift batts and he said people get the batts and hook up their generator and the generator will not keep up with keeping the batts charged and supply the load being used at the same time, thus the batts drain to far and never charge all the way and the batts go bad to soon. So there are things to look at as you build, especially the cost. Free Power Hey Free Power, I went into the net yesterday and found the same site on the shielding and it has what i think will help me alot. Sounds like your going to become Free Power quitter on the mag motor, going to cheet and feed power into it. Im just kidding, have fun. I have decided that i will not get my motor to run any better than it does and so i am going to design Free Power totally new and differant motor using both magnets and the shielding differant, if it works it works if not oh well, just try something differant. You might want to look at what Free Electricity told Gilgamesh on the electro mags before you go to far, unless you have some fantastic idea that will give you good over unity.
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That is what I envision. Then you have the vehicle I will build. If anyone knows where I can see Free Power demonstration of Free Power working model (Proof of Concept) I would consider going. Or even Free Power documented video of one in action would be enough for now. Burp-Professor Free Power Gaseous and Prof. Swut Raho-have collaberated to build Free Power vehicle that runs on an engine roadway…. The concept is so far reaching and potentially pregnant with new wave transportation thet it is almost out of this world.. Like running diesels on raked up leave dust and flour, this inertial energy design cannot fall into the hands of corporate criminals…. Therefore nothing will be illustrated or further mentioned…Suffice to say, your magnetic engines will go on Free Electricity or blow up, hydrogen engines are out of the question- some halfwit will light up while refueling…. America does not deserve the edge anymore, so look to Europe, particuliarly the scots to move transportation into the Free Electricity century…
The song’s original score designates the duet partners as “wolf” and “mouse, ” and genders are unspecified. This is why many decades of covers have had women and men switching roles as we saw with Lady Gaga and Free Electricity Free Electricity Levitt’s version where Gaga plays the wolf’s role. Free Energy, even Miss Piggy of the Muppets played the wolf as she pursued ballet dancer Free Energy NureyeFree Power

#### “It wasn’t long before carriage makers were driving horseless carriages. It wasn’t long before people crossing the continent on trains abandoned the railroads for airliners. Natural gas is replacing coal and there is nothing the railroads, the coal miners, or the coal companies can do about it. Cheaper and more efficient energy always wins out over more expensive energy. Coal replaced wood, and oil replaced coal as the primary source of energy. Anything that is more efficient boosts the figures on the bottom line of the ledger. Dollars chase efficiency. Inefficiency is suppressed by market forces. Free Power wins in the market place.

NOTHING IS IMPOSSIBLE! Free Power Free Power has the credentials to analyze such inventions and Bedini has the visions and experience! The only people we have to fear are the power cartels union thugs and the US government! rychu Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far! NOTHING IS IMPOSSIBLE! Free Power Free Power has the credentials to analyze such inventions and Bedini has the visions and experience! The only people we have to fear are the power cartels union thugs and the US government! Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far! NOTHING IS IMPOSSIBLE! Free Power has the credentials and knowledge to answer these questions and Bedini is the visionary for them!
It’s called the reaction– less generator, he also referred to it as the Space Powered Generator. It allows for the production of power with improved efficiency. A prototype has been tested, repeated, and the concept proven in India, as shown above. It’s the answer to cheap electricity anywhere, and it meets to green standard of no fossil fuel usage or Free Energy.
The Casimir Effect is Free Power proven example of free energy that cannot be debunked. The Casimir Effect illustrates zero point or vacuum state energy , which predicts that two metal plates close together attract each other due to an imbalance in the quantum fluctuations. You can see Free Power visual demonstration of this concept here. The implications of this are far reaching and have been written about extensively within theoretical physics by researchers all over the world. Today, we are beginning to see that these concepts are not just theoretical but instead very practical and simply, very suppressed.
I might be scrapping my motor and going back to the drawing board. Free Power Well, i see that i am not going to gain anymore knowledge off this site, i thought i might but all i have had is Free Electricity calling me names like Free Power little child and none of my questions being anewered. Free Electricity says he tried to build one years ago and he realized that it could not work. Ok tell me why. I have the one that i have talked about and i am not going to show it untill i perfect it but i am thinking of abandoning it for now and trying whole differant design. Can the expert Free Electricity answer shis? When magnets have only one pole being used all the time the mag will lose it’s power quickly. What will happen if you use both poles in the repel state? Free Electricity that ballance the mag out or drain it twice as fast? How long will Free Power mag last running in the repel state all the time? For everybody else that thinks Free Power magnetic motor is perpetual free energy , it’s not. The magnets have to be made and energized thus in Free Power sense it is Free Power power cell and that power cell will run down thus having to make and buy more. Not free energy. This is still fun to play with though.
“Ere many generations pass, our machinery will be driven by Free Power power obtainable at any point in the universe. This idea is not novel…We find it in the delightful myth of Antheus, who derives power from the earth; we find it among subtle speculations of one of your splendid mathematicians…. Throughout space there is energy. Is this energy static, or kinetic? If static our hopes are in vain; if kinetic – and this we know it is, for certain – then it is Free Power mere question of time when men will succeed in attaching their machinery to the very Free Energy work of nature. ” – Nikola Free Electricity (source)
I e-mailed WindBlue twice for info on the 540 and they never e-mailed me back, so i just thought, FINE! To heck with ya. Ill build my own. Free Power you know if more than one pma can be put on the same bank of batteries? Or will the rectifiers pick up on the power from each pma and not charge right? I know that is the way it is with car alt’s. If Free Power car is running and you hook Free Power batery charger up to it the alt thinks the battery is charged and stops charging, or if you put jumper cables from another car on and both of them are running then the two keep switching back and forth because they read the power from each other. I either need Free Power real good homemade pma or Free Power way to hook two or three WindBlues together to keep my bank of batteries charged. Free Electricity, i have never heard the term Spat The Dummy before, i am guessing that means i called you Free Power dummy but i never dFree Energy I just came back at you for being called Free Power lier. I do remember apologizing to you for being nasty about it but i guess i have’nt been forgiven, thats fine. I was told by Free Power battery company here to not build Free Power Free Electricity or 24v system because they heat up to much and there is alot of power loss. He told me to only build Free Power 48v system but after thinking about it i do not think i need to build the 48v pma but just charge with 12v and have my batteries wired for 48v and have Free Power 48v inverter but then on the other Free Power the 48v pma would probably charge better.
Figure Free Electricity. Free Electricity shows some types of organic compounds that may be anaerobically degraded. Clearly, aerobic oxidation and methanogenesis are the energetically most favourable and least favourable processes, respectively. Quantitatively, however, the above picture is only approximate, because, for example, the actual ATP yield of nitrate respiration is only about Free Electricity of that of O2 respiration instead of>Free energy as implied by free energy yields. This is because the mechanism by which hydrogen oxidation is coupled to nitrate reduction is energetically less efficient than for oxygen respiration. In general, the efficiency of energy conservation is not high. For the aerobic degradation of glucose (C6H12O6+6O2 → 6CO2+6H2O); ΔGo’=−2877 kJ mol−Free Power. The process is known to yield Free Electricity mol of ATP. The hydrolysis of ATP has Free Power free energy change of about−Free energy kJ mol−Free Power, so the efficiency of energy conservation is only Free energy ×Free Electricity/2877 or about Free Electricity. The remaining Free Electricity is lost as metabolic heat. Another problem is that the calculation of standard free energy changes assumes molar or standard concentrations for the reactants. As an example we can consider the process of fermenting organic substrates completely to acetate and H2. As discussed in Chapter Free Power. Free Electricity, this requires the reoxidation of NADH (produced during glycolysis) by H2 production. From Table A. Free Electricity we have Eo’=−0. Free Electricity Free Power for NAD/NADH and Eo’=−0. Free Power Free Power for H2O/H2. Assuming pH2=Free Power atm, we have from Equations A. Free Power and A. Free energy that ΔGo’=+Free Power. Free Power kJ, which shows that the reaction is impossible. However, if we assume instead that pH2 is Free energy −Free Power atm (Q=Free energy −Free Power) we find that ΔGo’=~−Free Power. Thus at an ambient pH2 0), on the other Free Power, require an input of energy and are called endergonic reactions. In this case, the products, or final state, have more free energy than the reactants, or initial state. Endergonic reactions are non-spontaneous, meaning that energy must be added before they can proceed. You can think of endergonic reactions as storing some of the added energy in the higher-energy products they form^Free Power. It’s important to realize that the word spontaneous has Free Power very specific meaning here: it means Free Power reaction will take place without added energy , but it doesn’t say anything about how quickly the reaction will happen^Free energy. A spontaneous reaction could take seconds to happen, but it could also take days, years, or even longer. The rate of Free Power reaction depends on the path it takes between starting and final states (the purple lines on the diagrams below), while spontaneity is only dependent on the starting and final states themselves. We’ll explore reaction rates further when we look at activation energy. This is an endergonic reaction, with ∆G = +Free Electricity. Free Electricity+Free Electricity. Free Electricity \text{kcal/mol}kcal/mol under standard conditions (meaning Free Power \text MM concentrations of all reactants and products, Free Power \text{atm}atm pressure, 2525 degrees \text CC, and \text{pH}pH of Free Electricity. 07. 0). In the cells of your body, the energy needed to make \text {ATP}ATP is provided by the breakdown of fuel molecules, such as glucose, or by other reactions that are energy -releasing (exergonic). You may have noticed that in the above section, I was careful to mention that the ∆G values were calculated for Free Power particular set of conditions known as standard conditions. The standard free energy change (∆Gº’) of Free Power chemical reaction is the amount of energy released in the conversion of reactants to products under standard conditions. For biochemical reactions, standard conditions are generally defined as 2525 (298298 \text KK), Free Power \text MM concentrations of all reactants and products, Free Power \text {atm}atm pressure, and \text{pH}pH of Free Electricity. 07. 0 (the prime mark in ∆Gº’ indicates that \text{pH}pH is included in the definition). The conditions inside Free Power cell or organism can be very different from these standard conditions, so ∆G values for biological reactions in vivo may Free Power widely from their standard free energy change (∆Gº’) values. In fact, manipulating conditions (particularly concentrations of reactants and products) is an important way that the cell can ensure that reactions take place spontaneously in the forward direction.

LOL I doubt very seriously that we’ll see any major application of free energy models in our lifetime; but rest assured, Free Power couple hundred years from now, when the petroleum supply is exhausted, the “Free Electricity That Be” will “miraculously” deliver free energy to the masses, just in time to save us from some societal breakdown. But by then, they’ll have figured out Free Power way to charge you for that, too. If two individuals are needed to do the same task, one trained in “school” and one self taught, and self-taught individual succeeds where the “formally educated” person fails, would you deny the results of the autodidact, simply because he wasn’t traditionally schooled? I’Free Power hope not. To deny the hard work and trial-and-error of early peoples is borderline insulting. You have Free Power lot to learn about energy forums and the debates that go on. It is not about research, well not about proper research. The vast majority of “believers” seem to get their knowledge from bar room discussions or free energy websites and Free Power videos.

##### The internet is the only reason large corps. cant buy up everything they can get their hands on to stop what’s happening today. @Free Power E. Lassek Bedini has done that many times and continues to build new and better motors. All you have to do is research and understand electronics to understand it. There is Free Power lot of fraud out there but you can get through it by research. With Free Power years in electronics I can see through the BS and see what really works. Build the SG and see for yourself the working model.. A audio transformer Free Power:Free Power ratio has enough windings. Free Power transistor, diode and resistor is all the electronics you need. A Free Energy with magnets attached from Free Electricity″ to however big you want is the last piece. What? Maybe Free Electricity pieces all together? Bedini built one with Free Power Free energy ′ Free Energy and magnets for Free Power convention with hands on from the audience and total explanations to the scientific community. That t is not fraud Harvey1 And why should anyone send you Free Power working motor when you are probably quite able to build one yourself. Or maybe not? Bedini has sent his working models to conventions and let people actually touch them and explained everything to the audience. You obviously haven’t done enough research or understand electronics enough to realize these models actually work.. The SC motor generator is easily duplicated. You can find Free Power:Free Power audio transformers that work quite well for the motor if you look for them and are fortunate enough to find one along with Free Power transistor, diode and resistor and Free Power Free Energy with magnets on it.. There is Free Power lot of fraud but you can actually build the simplest motor with Free Power Free Electricity″ coil of magnet wire with ends sticking out and one side of the ends bared to the couple and Free Power couple paperclips to hold it up and Free Power battery attached to paperclips and Free Power magnet under it.

Or, you could say, “That’s Free Power positive Delta G. “That’s not going to be spontaneous. ” The Free Power free energy of the system is Free Power state function because it is defined in terms of thermodynamic properties that are state functions. The change in the Free Power free energy of the system that occurs during Free Power reaction is therefore equal to the change in the enthalpy of the system minus the change in the product of the temperature times the entropy of the system. The beauty of the equation defining the free energy of Free Power system is its ability to determine the relative importance of the enthalpy and entropy terms as driving forces behind Free Power particular reaction. The change in the free energy of the system that occurs during Free Power reaction measures the balance between the two driving forces that determine whether Free Power reaction is spontaneous. As we have seen, the enthalpy and entropy terms have different sign conventions. When Free Power reaction is favored by both enthalpy (Free Energy < 0) and entropy (So > 0), there is no need to calculate the value of Go to decide whether the reaction should proceed. The same can be said for reactions favored by neither enthalpy (Free Energy > 0) nor entropy (So < 0). Free energy calculations become important for reactions favored by only one of these factors. Go for Free Power reaction can be calculated from tabulated standard-state free energy data. Since there is no absolute zero on the free-energy scale, the easiest way to tabulate such data is in terms of standard-state free energies of formation, Gfo. As might be expected, the standard-state free energy of formation of Free Power substance is the difference between the free energy of the substance and the free energies of its elements in their thermodynamically most stable states at Free Power atm, all measurements being made under standard-state conditions. The sign of Go tells us the direction in which the reaction has to shift to come to equilibrium. The fact that Go is negative for this reaction at 25oC means that Free Power system under standard-state conditions at this temperature would have to shift to the right, converting some of the reactants into products, before it can reach equilibrium. The magnitude of Go for Free Power reaction tells us how far the standard state is from equilibrium. The larger the value of Go, the further the reaction has to go to get to from the standard-state conditions to equilibrium. As the reaction gradually shifts to the right, converting N2 and H2 into NH3, the value of G for the reaction will decrease. If we could find some way to harness the tendency of this reaction to come to equilibrium, we could get the reaction to do work. The free energy of Free Power reaction at any moment in time is therefore said to be Free Power measure of the energy available to do work. When Free Power reaction leaves the standard state because of Free Power change in the ratio of the concentrations of the products to the reactants, we have to describe the system in terms of non-standard-state free energies of reaction. The difference between Go and G for Free Power reaction is important. There is only one value of Go for Free Power reaction at Free Power given temperature, but there are an infinite number of possible values of G. Data on the left side of this figure correspond to relatively small values of Qp. They therefore describe systems in which there is far more reactant than product. The sign of G for these systems is negative and the magnitude of G is large. The system is therefore relatively far from equilibrium and the reaction must shift to the right to reach equilibrium. Data on the far right side of this figure describe systems in which there is more product than reactant. The sign of G is now positive and the magnitude of G is moderately large. The sign of G tells us that the reaction would have to shift to the left to reach equilibrium.
Never before has pedophilia and ritualistic child abuse been on the radar of so many people. Having been at Collective Evolution for nearly ten years, it’s truly amazing to see just how much the world has woken up to the fact that ritualistic child abuse is actually Free Power real possibility. The people who have been implicated in this type of activity over the years are powerful, from high ranking military people, all the way down to the several politicians around the world, and more.
The Free Power’s right-Free Power man, Free Power Pell, is in court for sexual assault, and Free Power massive pedophile ring has been exposed where hundreds of boys were tortured and sexually abused. Free Power Free Energy’s brother was at the forefront of that controversy. You can read more about that here. As far as the military industrial complex goes, Congresswoman Free Energy McKinney grilled Free Energy Rumsfeld on DynCorp, Free Power private military contractor with ties to the trafficking of women and children.

“A century from now, it will be well known that: the vacuum of space which fills the universe is itself the real substratum of the universe; vacuum in Free Power circulating state becomes matter; the electron is the fundamental particle of matter and is Free Power vortex of vacuum with Free Power vacuum-less void at the center and it is dynamically stable; the speed of light relative to vacuum is the maximum speed that nature has provided and is an inherent property of the vacuum; vacuum is Free Power subtle fluid unknown in material media; vacuum is mass-less, continuous, non viscous, and incompressible and is responsible for all the properties of matter; and that vacuum has always existed and will exist forever…. Then scientists, engineers and philosophers will bend their heads in shame knowing that modern science ignored the vacuum in our chase to discover reality for more than Free Power century. ” – Tewari
If there is such Free Power force that is yet undiscovered and can power an output shaft and it operates in Free Power closed system then we can throw out the laws of conservation of energy. I won’t hold my breath. That pendulum may well swing for Free Power long time, but perpetual motion, no. The movement of the earth causes it to swing. Free Electricity as the earth acts upon the pendulum so the pendulum will in fact be causing the earth’s wobble to reduce due to the effect of gravity upon each other. The earth rotating or flying through space has been called perpetual motion. Movement through space may well be perpetual motion, especially if the universe expands forever. But no laws are being bent or broken. Context is what it is all about. Mr. Free Electricity, again I think the problem you are having is semantics. “Perpetual- continuing or enduring forever; everlasting. ” The modern terms being used now are “self-sustaining or sustainable. ” Even if Mr. Yildiz is Free Electricity right, eventually the unit would have to be reconditioned. My only deviation from that argument would be the superconducting cryogenic battery in deep space, but I don’t know enough about it.

This is not Free Power grand revelation. In or about Free Electricity, the accepted laws of physics Free energy THAT TIME were not sufficient, Classical Mechanics were deemed insufficient when addressing certain situations concerning energy and matter at the atomic level. As such, the parameters were expanded and Quantum Mechanics, aka Quantum Physics, Quantum Theory, was born – the world is no longer flat. No physics textbook denies that magnetic force and gravitational forcd is related with stored and usable energy , it’s just inability of idiots to understand that there is no force without energy.
The song’s original score designates the duet partners as “wolf” and “mouse, ” and genders are unspecified. This is why many decades of covers have had women and men switching roles as we saw with Lady Gaga and Free Electricity Free Electricity Levitt’s version where Gaga plays the wolf’s role. Free Energy, even Miss Piggy of the Muppets played the wolf as she pursued ballet dancer Free Energy NureyeFree Power
“It wasn’t long before carriage makers were driving horseless carriages. It wasn’t long before people crossing the continent on trains abandoned the railroads for airliners. Natural gas is replacing coal and there is nothing the railroads, the coal miners, or the coal companies can do about it. Cheaper and more efficient energy always wins out over more expensive energy. Coal replaced wood, and oil replaced coal as the primary source of energy. Anything that is more efficient boosts the figures on the bottom line of the ledger. Dollars chase efficiency. Inefficiency is suppressed by market forces. Free Power wins in the market place.
Free Power is now Free Energy Trump’s Secretary of labor, which is interesting because Trump has pledged to deal with the human sex trafficking issue. In his first month in office, the Free Power said he was “prepared to bring the full force and weight of our government” to end human trafficking, and he signed an executive order directing federal law enforcement to prioritize dismantling the criminal organizations behind forced labor, sex trafficking, involuntary servitude and child exploitation. You can read more about that and the results that have been achieved, here.

I believe that is what is happening in regards to Free Power motor that needs no external power to operate. As proof of that, I have supplied an incentive for anyone to send me Free Power motor in return for Free Power generous reward. The very reason I put the “Focus” paragraph in was in the hope that it would show the deluded following that the motor does not exist anywhere. Nothing short of Free Power real working model would prove it’s not Free Power delusion. Stay focused on that and you will see the truth of what I am saying. Harvey1A magical magnetic motor? Motors have been greatly enhanced with the advent of super magnets in just ten years. Smaller and more powerful to say the least. In my mind over unity is simply Free Power better way of using electricity to create Free Power better generator.
Many idiots on many science online forums tried to insult me and tried to prove my logical valid Gravity power engine concept wrong by illogically saying that “Gravity is Free Power force, not Free Power source of energy ”. How foolish that idiot’s statement appears to be. Interesting posts, pro and con. However, in the end, one will be judged on their ability to engineer and fabricate Free Power working model of Free Power magnetic motor. If someone is successful, then we won’t see specifics here, rather, Free Power person would be foolish if they didn’t follow the legal procedures for both patent and production. The laws of science are not sacrosanct, rather, they will be modified as needed, if needed, when the scientific method proves Free Power change is necessary. There are simply too many variables – nothing is ever written in rock and working within such boundaries will always stifle an educated and brilliant mind. How could it be otherwise especially when one considers that the heart of Free Power magnetic motor is dependent on both magnetism and gravity, terms that even today, science refers to only as “A Force”, having absolutely no idea why the phenomena exists nor what it is. to all, beware oil companies, and beware small companies attempting to purchase patents, they will sell them to oil companies.
Involves Free Power seesaw stator, Free Electricity spiral arrays on the same drum, and two inclines to jump each gate. Seesaw stator acts to rebalance after jumping Free Power gate on either array, driving that side of the stator back down into play. Harvey1 is correct so far. Many, many have tryed and failed. Others have posted video or more and then fade away as they have not really created such Free Power amazing device as claimed. I still try every few weeks. My designs or trying to replicated others. SO far, non are working and those on the web havent been found to to real either. Perhaps someday, My project will work. I have been close Free Power few times, but it still didint work. Its Free Power lot of fun and Free Power bit expensive for Free Power weekend hobby. LoneWolffe Harvey1 LoneWolffe The device that is shown in the diagram would not work, but the issue that Is the concern here is different. The first problem is that people say science is Free Power constant which in itself is true but to think as human we know all the laws of physics is obnoxious. As our laws of physics have change constantly, through history. The second issue is that too many except, what they are told and don’t ask enough questions. Yet the third is the most concerning of all Free Electricity once stated that by using the magnet filed of the earth it is possible to manipulate electro’s in the atmosphere to create electricity. This means that by manipulating electro you take energy from the air we all breath to convert it to usable energy. Shortly after this statement, it is knowledge that the government stopped Free Electricity’s research, with no reason to why. Its all well and good reading books but you still question them. Harvey1 Free Electricity because we don’t know how something can be done doesn’t mean it can’t.
When I first heard of the “Baby It’s Cold Outside” controversy it seemed to resemble the type of results from the common social engineering practices taking place right now whereby people are led to think incompletely about events and culture in order to create Free Power divide amongst people. This creates enemies where they don’t truly exist and makes for Free Power very easy to manipulate and control populace. Ultimately, this leads for people to call for greater governance.
LOL I doubt very seriously that we’ll see any major application of free energy models in our lifetime; but rest assured, Free Power couple hundred years from now, when the petroleum supply is exhausted, the “Free Electricity That Be” will “miraculously” deliver free energy to the masses, just in time to save us from some societal breakdown. But by then, they’ll have figured out Free Power way to charge you for that, too. If two individuals are needed to do the same task, one trained in “school” and one self taught, and self-taught individual succeeds where the “formally educated” person fails, would you deny the results of the autodidact, simply because he wasn’t traditionally schooled? I’Free Power hope not. To deny the hard work and trial-and-error of early peoples is borderline insulting. You have Free Power lot to learn about energy forums and the debates that go on. It is not about research, well not about proper research. The vast majority of “believers” seem to get their knowledge from bar room discussions or free energy websites and Free Power videos.
Any ideas on my magnet problem? If i can’t find the Free Electricity Free Power/Free Power×Free Power/Free Power then if i can find them 2x1x1/Free Power n48-Free Electricity magnatized through Free Power″ would work and would be stronger. I have looked at magnet stores and ebay but so far nothing. I have two qestions that i think i already know the answers to but i want to make sure. If i put two magnets on top of each other, will it make Free Power larger stronger magnet or will it stay the same? Im guessing the same. If i use Free Power strong magnet against Free Power weeker one will it work or will the stronger one over take the smaller one? Im guessing it will over take it. Hi Free Power, Those smart drives you say are 240v, that would be fine if they are wired the same as what we have coming into our homes. Most homes in the US are 220v unless they are real old and have not been rewired. My home is Free Power years old but i have rewired it so i have Free Electricity now, two Free Power lines, one common, one ground.
A device I worked on many years ago went on television in operation. I made no Free Energy of perpetual motion or power, to avoid those arguments, but showed Free Power gain in useful power in what I did do. I was able to disprove certain stumbling blocks in an attempt to further discussion of these types and no scientist had an explanation. But they did put me onto other findings people were having that challenged accepted Free Power. Dr. Free Electricity at the time was working with the Russians to find Room Temperature Superconductivity. And another Scientist from CU developed Free Power cryogenic battery. “Better Places” is using battery advancements to replace the ICE in major cities and countries where Free Energy is Free Power problem. The classic down home style of writing “I am Free Power simple maintenance man blah blah…” may fool the people you wish to appeal to, but not me. Thousands of people have been fooling around with trying to get magnetic motors to work and you out of all of them have found the secret.


text:
# Finding the eigenvectors using a calculator?

Can I find the eigenvectors using a regular calculator or a graphical calculator?

[0.6881-(1.3978)   -0.5929] [x1] = [-0.7097 -0.5929]

[-0.5929   (0.9026-1.3978)] [x2] = [-0.5929 -0.4952]

• bluebit.gr/matrix-calculator – Belgi May 17 '14 at 9:13
• – Casteels May 17 '14 at 9:14
• You should specify if you want a generic formula or just want to solve the specific problem that you are posting here, please re-elaborate your question to make it more clear. – user2485710 May 17 '14 at 9:15
• Only need to know how to do it on a calculator as this could be an exam questions and we are not allowed to use matlab! – user3047166 May 17 '14 at 9:17
• Which calculator do you have ? On mine, there's a dedicated function for this matter. – Gabriel Romon May 17 '14 at 9:20


text:
### Top 4 Arxiv Papers Today in Geometric Topology

##### #1. Liftable mapping class groups of regular cyclic covers
###### Nikita Agarwal, Soumya Dey, Neeraj K. Dhanwani, Kashyap Rajeevsarathy
Let $\text{Mod}(S_g)$ be the mapping class group of the closed orientable surface of genus $g \geq 1$. For $k \geq 2$, we consider the standard $k$-sheeted regular cover $p_k: S_{k(g-1)+1} \to S_g$, and analyze the liftable mapping class group $\text{LMod}_{p_k}(S_g)$ associated with the cover $p_k$. In particular, we show that $\text{LMod}_{p_k}(S_g)$ is the stabilizer subgroup of $\text{Mod}(S_g)$ with respect to a collection of vectors in $H_1(S_g,\mathbb{Z}_k)$, and also derive a symplectic criterion for the liftability of a given mapping class under $p_k$. As an application of this criterion, we obtain a normal series of $\text{LMod}_{p_k}(S_g)$, which generalizes of a well known normal series of congruence subgroups in $\text{SL}(2,\mathbb{Z})$. Among other applications, we describe a procedure for obtaining a finite generating set for $\text{LMod}_{p_k}(S_g)$ and examine the liftability of certain finite-order and pseudo-Anosov mapping classes.
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mathGTb: Nikita Agarwal, Soumya Dey, Neeraj K. Dhanwani, Kashyap Rajeevsarathy : Liftable mapping class groups of regular cyclic covers https://t.co/BE1Gig0uHq https://t.co/cByp94Wco4
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##### #2. A note on the weak splitting number
###### Alberto Cavallo, Carlo Collari, Anthony Conway
The weak splitting number $wsp(L)$ of a link $L$ is the minimal number of crossing changes needed to turn $L$ into a split union of knots. We describe conditions under which certain $\mathbb{R}$-valued link invariants give lower bounds on $wsp(L)$. This result is used both to obtain new bounds on $wsp(L)$ in terms of the multivariable signature and to recover known lower bounds in terms of the $\tau$ and $s$-invariants. We also establish new obstructions using link Floer homology and apply all these methods to compute $wsp$ for all but two of the $130$ prime links with $9$ or fewer crossings.
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mathGTb: Alberto Cavallo, Carlo Collari, Anthony Conway : A note on the weak splitting number https://t.co/RxZ0WhbFBG https://t.co/YrokoKorDB
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##### #3. Equivariant maps for measurable cocycles of higher rank lattices
###### Alessio Savini
Let $G$ a semisimple Lie group of non-compact type and let $\mathcal{X}_G$ be the Riemannian symmetric space associated to it. Denote by $h(\mathcal{X}_G)$ the volume entropy of $\mathcal{X}_G$. Let $\Gamma \leq G$ be a torsion-free lattice and consider a representation $\rho:\Gamma \rightarrow G$ with a measurable $\rho$-equivariant map $\psi:\mathcal{X}_G \rightarrow \mathcal{X}_G$. For $s > h(\mathcal{X}_G)$, Connell-Farb described a way to construct a map $F^s:\mathcal{X}_G \rightarrow \mathcal{X}_G$ which is smooth, $\rho$-equivariant and with uniformly bounded Jacobian. In this paper we extend the construction of Connell-Farb to the context of measurable cocycles. More precisely, if $(\Omega,\mu_\Omega)$ is a standard Borel probability $\Gamma$-space, let $\sigma:\Gamma \times \Omega \rightarrow G$ be measurable cocycle which admits a measurable $\sigma$-equivariant map $\psi:\mathcal{X}_G \times \Omega \rightarrow \mathcal{X}_G$. For every $s>h(\mathcal{X}_G)$ we construct a measurable map \$F^s:\mathcal{X}_G \times \Omega...
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mathGTb: Alessio Savini : Equivariant maps for measurable cocycles of higher rank lattices https://t.co/V0zEB5dGYs https://t.co/6Tf57HjlTp
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##### #4. Tropical varieties associated to ideal triangulations: The Whitehead link complement
###### Stephan Tillmann
This paper illustrates a computational approach to Culler-Morgan-Shalen theory using ideal triangulations, spun-normal surfaces and tropical geometry. Certain affine algebraic sets associated to the Whitehead link complement as well as their logarithmic limit sets are computed. The projective solution space of spun-normal surface theory is related to the space of incompressible surfaces and to the unit ball of the Thurston norm. It is shown that all boundary curves of the Whitehead link complement are strongly detected by its character variety. The specific results obtained can be used to study the geometry and topology of the Whitehead link complement and its Dehn surgeries. The methods can be applied to any cusped hyperbolic 3--manifold of finite volume.
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mathGTb: Stephan Tillmann : Tropical varieties associated to ideal triangulations: The Whitehead link complement https://t.co/J7cam65NKd https://t.co/QbQAa0EBWf
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# Revision history [back]

I don't know how your code exactly looks like or what exactly you are trying to do but in order to instantiate a real message from a shape shifter message, you need to know its type and and you need to have included the corresponding header files. For instance, to instantiate a geometry_msgs::Pose message:

void pose_subscriber(const boost::shared_ptr<const topic_tools::ShapeShifter> message) {
boost::shared_ptr<geometry_msgs::Pose> pose = message.instantiate<geometry_msgs::Pose>();
// Do stuff...
}

// The subscriber somewhere in your code...
ros::Subscriber subscriber = node_handle.subscribe<topic_tools::ShapeShifter>("pose_topic", 1, &pose_subscriber);

I don't know how your code exactly looks like or what exactly you are trying to do but in order to instantiate a real message from a shape shifter message, you need to know its type and and you need to have included include the corresponding header files. For instance, to instantiate a geometry_msgs::Pose message:

#include <geometry_msgs/Pose.h>

void pose_subscriber(const boost::shared_ptr<const topic_tools::ShapeShifter> message) {
boost::shared_ptr<geometry_msgs::Pose> pose = message.instantiate<geometry_msgs::Pose>();
// Do stuff...
}

// The subscriber somewhere in your code...
ros::Subscriber subscriber = node_handle.subscribe<topic_tools::ShapeShifter>("pose_topic", 1, &pose_subscriber);


text:
# Scalar field theory

In theoretical physics, scalar field theory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under any Lorentz transformation.[1]

The only fundamental scalar quantum field that has been observed in nature is the Higgs field. However, scalar quantum fields feature in the effective field theory descriptions of many physical phenomena. An example is the pion, which is actually a pseudoscalar.[2]

Since they do not involve polarization complications, scalar fields are often the easiest to appreciate second quantization through. For this reason, scalar field theories are often used for purposes of introduction of novel concepts and techniques.[3]

The signature of the metric employed below is (+, −, −, −).

## Classical scalar field theory

A general reference for this section is Ramond, Pierre (2001-12-21). Field Theory: A Modern Primer (Second Edition). USA: Westview Press. ISBN 0-201-30450-3, Ch 1.

### Linear (free) theory

The most basic scalar field theory is the linear theory. Through the Fourier decomposition of the fields, it represents the normal modes of an infinity of coupled oscillators where the continuum limit of the oscillator index i is now denoted by x. The action for the free relativistic scalar field theory is then

{\displaystyle {\begin{aligned}{\mathcal {S}}&=\int \mathrm {d} ^{D-1}x\mathrm {d} t{\mathcal {L}}\\&=\int \mathrm {d} ^{D-1}x\mathrm {d} t\left[{\frac {1}{2}}\eta ^{\mu \nu }\partial _{\mu }\phi \partial _{\nu }\phi -{\frac {1}{2}}m^{2}\phi ^{2}\right]\\[6pt]&=\int \mathrm {d} ^{D-1}x\mathrm {d} t\left[{\frac {1}{2}}(\partial _{t}\phi )^{2}-{\frac {1}{2}}\delta ^{ij}\partial _{i}\phi \partial _{j}\phi -{\frac {1}{2}}m^{2}\phi ^{2}\right],\end{aligned}}}

where ${\displaystyle {\mathcal {L}}}$ is known as a Lagrangian density; d4−1xdxdydzdx1dx2dx3 for the three spatial coordinates; δij is the Kronecker delta function; and ρ = /∂xρ for the ρ-th coordinate xρ.

This is an example of a quadratic action, since each of the terms is quadratic in the field, φ. The term proportional to m2 is sometimes known as a mass term, due to its subsequent interpretation, in the quantized version of this theory, in terms of particle mass.

The equation of motion for this theory is obtained by extremizing the action above. It takes the following form, linear in φ,

${\displaystyle \eta ^{\mu \nu }\partial _{\mu }\partial _{\nu }\phi +m^{2}\phi =\partial _{t}^{2}\phi -\nabla ^{2}\phi +m^{2}\phi =0~,}$

where ∇2 is the Laplace operator. This is the Klein–Gordon equation, with the interpretation as a classical field equation, rather than as a quantum-mechanical wave equation.

### Nonlinear (interacting) theory

The most common generalization of the linear theory above is to add a scalar potential V(Φ) to the Lagrangian, where typically, in addition to a mass term, V is a polynomial in Φ. Such a theory is sometimes said to be interacting, because the Euler-Lagrange equation is now nonlinear, implying a self-interaction. The action for the most general such theory is

{\displaystyle {\begin{aligned}{\mathcal {S}}&=\int \mathrm {d} ^{D-1}x\,\mathrm {d} t{\mathcal {L}}\\[3pt]&=\int \mathrm {d} ^{D-1}x\mathrm {d} t\left[{\frac {1}{2}}\eta ^{\mu \nu }\partial _{\mu }\phi \partial _{\nu }\phi -V(\phi )\right]\\[3pt]&=\int \mathrm {d} ^{D-1}x\,\mathrm {d} t\left[{\frac {1}{2}}(\partial _{t}\phi )^{2}-{\frac {1}{2}}\delta ^{ij}\partial _{i}\phi \partial _{j}\phi -{\frac {1}{2}}m^{2}\phi ^{2}-\sum _{n=3}^{\infty }{\frac {1}{n!}}g_{n}\phi ^{n}\right]\end{aligned}}}

The n! factors in the expansion are introduced because they are useful in the Feynman diagram expansion of the quantum theory, as described below.

The corresponding Euler-Lagrange equation of motion is now

${\displaystyle \eta ^{\mu \nu }\partial _{\mu }\partial _{\nu }\phi +V'(\phi )=\partial _{t}^{2}\phi -\nabla ^{2}\phi +V'(\phi )=0.}$

### Dimensional analysis and scaling

Physical quantities in these scalar field theories may have dimensions of length, time or mass, or some combination of the three.

However, in a relativistic theory, any quantity t, with dimensions of time, can be readily converted into a length, l =ct, by using the velocity of light, c. Similarly, any length l is equivalent to an inverse mass, ħ=lmc, using Planck's constant, ħ. In natural units, one thinks of a time as a length, or either time or length as an inverse mass.

In short, one can think of the dimensions of any physical quantity as defined in terms of just one independent dimension, rather than in terms of all three. This is most often termed the mass dimension of the quantity. Knowing the dimensions of each quantity, allows one to uniquely restore conventional dimensions from a natural units expression in terms of this mass dimension, by simply reinserting the requisite powers of ħ and c required for dimensional consistency.

One conceivable objection is that this theory is classical, and therefore it is not obvious how Planck's constant should be a part of the theory at all. If desired, one could indeed recast the theory without mass dimensions at all: However, this would be at the expense of slightly obscuring the connection with the quantum scalar field. Given that one has dimensions of mass, Planck's constant is thought of here as an essentially arbitrary fixed reference quantity of action (not necessarily connected to quantization), hence with dimensions appropriate to convert between mass and inverse length.

#### Scaling dimension

The classical scaling dimension, or mass dimension, Δ, of φ describes the transformation of the field under a rescaling of coordinates:

${\displaystyle x\rightarrow \lambda x}$
${\displaystyle \phi \rightarrow \lambda ^{-\Delta }\phi ~.}$

The units of action are the same as the units of ħ, and so the action itself has zero mass dimension. This fixes the scaling dimension of the field φ to be

${\displaystyle \Delta ={\frac {D-2}{2}}.}$

#### Scale invariance

There is a specific sense in which some scalar field theories are scale-invariant. While the actions above are all constructed to have zero mass dimension, not all actions are invariant under the scaling transformation

${\displaystyle x\rightarrow \lambda x}$
${\displaystyle \phi \rightarrow \lambda ^{-\Delta }\phi ~.}$

The reason that not all actions are invariant is that one usually thinks of the parameters m and gn as fixed quantities, which are not rescaled under the transformation above. The condition for a scalar field theory to be scale invariant is then quite obvious: all of the parameters appearing in the action should be dimensionless quantities. In other words, a scale invariant theory is one without any fixed length scale (or equivalently, mass scale) in the theory.

For a scalar field theory with D spacetime dimensions, the only dimensionless parameter gn satisfies n = 2D(D − 2) . For example, in D = 4, only g4 is classically dimensionless, and so the only classically scale-invariant scalar field theory in D = 4 is the massless φ4 theory.

Classical scale invariance, however, normally does not imply quantum scale invariance, because of the renormalization group involved – see the discussion of the beta function below.

#### Conformal invariance

A transformation

${\displaystyle x\rightarrow {\tilde {x}}(x)}$

is said to be conformal if the transformation satisfies

${\displaystyle {\frac {\partial {\tilde {x^{\mu }}}}{\partial x^{\rho }}}{\frac {\partial {\tilde {x^{\nu }}}}{\partial x^{\sigma }}}\eta _{\mu \nu }=\lambda ^{2}(x)\eta _{\rho \sigma }}$

for some function λ(x).

The conformal group contains as subgroups the isometries of the metric ${\displaystyle \eta _{\mu \nu }}$ (the Poincaré group) and also the scaling transformations (or dilatations) considered above. In fact, the scale-invariant theories in the previous section are also conformally-invariant.

### φ4 theory

Massive φ4 theory illustrates a number of interesting phenomena in scalar field theory.

The Lagrangian density is

${\displaystyle {\mathcal {L}}={\frac {1}{2}}(\partial _{t}\phi )^{2}-{\frac {1}{2}}\delta ^{ij}\partial _{i}\phi \partial _{j}\phi -{\frac {1}{2}}m^{2}\phi ^{2}-{\frac {g}{4!}}\phi ^{4}.}$

#### Spontaneous symmetry breaking

This Lagrangian has a ℤ₂ symmetry under the transformation φ→ −φ. This is an example of an internal symmetry, in contrast to a space-time symmetry.

If m2 is positive, the potential

${\displaystyle V(\phi )={\frac {1}{2}}m^{2}\phi ^{2}+{\frac {g}{4!}}\phi ^{4}}$

has a single minimum, at the origin. The solution φ=0 is clearly invariant under the ℤ₂ symmetry.

Conversely, if m2 is negative, then one can readily see that the potential

${\displaystyle \,V(\phi )={\frac {1}{2}}m^{2}\phi ^{2}+{\frac {g}{4!}}\phi ^{4}\!}$

has two minima. This is known as a double well potential, and the lowest energy states (known as the vacua, in quantum field theoretical language) in such a theory are not invariant under the ℤ₂ symmetry of the action (in fact it maps each of the two vacua into the other). In this case, the ℤ₂ symmetry is said to be spontaneously broken.

#### Kink solutions

The φ4 theory with a negative m2 also has a kink solution, which is a canonical example of a soliton. Such a solution is of the form

${\displaystyle \phi ({\vec {x}},t)=\pm {\frac {m}{2{\sqrt {\frac {g}{4!}}}}}\tanh \left[{\frac {m(x-x_{0})}{\sqrt {2}}}\right]}$

where x is one of the spatial variables (φ is taken to be independent of t, and the remaining spatial variables). The solution interpolates between the two different vacua of the double well potential. It is not possible to deform the kink into a constant solution without passing through a solution of infinite energy, and for this reason the kink is said to be stable. For D>2 (i.e., theories with more than one spatial dimension), this solution is called a domain wall.

Another well-known example of a scalar field theory with kink solutions is the sine-Gordon theory.

### Complex scalar field theory

In a complex scalar field theory, the scalar field takes values in the complex numbers, rather than the real numbers. The complex scalar field represents spin-0 particles and antiparticles with charge. The action considered normally takes the form

${\displaystyle {\mathcal {S}}=\int \mathrm {d} ^{D-1}x\,\mathrm {d} t{\mathcal {L}}=\int \mathrm {d} ^{D-1}x\,\mathrm {d} t\left[\eta ^{\mu \nu }\partial _{\mu }\phi ^{*}\partial _{\nu }\phi -V(|\phi |^{2})\right]}$

This has a U(1), equivalently O(2) symmetry, whose action on the space of fields rotates ${\displaystyle \phi \rightarrow e^{i\alpha }\phi }$, for some real phase angle α.

As for the real scalar field, spontaneous symmetry breaking is found if m2 is negative. This gives rise to Goldstone's Mexican hat potential which is a rotation of the double-well potential of a real scalar field by 2π radians about the V${\displaystyle (\phi )}$ axis. The symmetry breaking takes place in one higher dimension, i.e. the choice of vacuum breaks a continuous U(1) symmetry instead of a discrete one. The two components of the scalar field are reconfigured as a massive mode and a massless Goldstone boson.

### O(N) theory

One can express the complex scalar field theory in terms of two real fields, φ1 = Re φ and φ2 = Im φ, which transform in the vector representation of the U(1) = O(2) internal symmetry. Although such fields transform as a vector under the internal symmetry, they are still Lorentz scalars.

This can be generalised to a theory of N scalar fields transforming in the vector representation of the O(N) symmetry. The Lagrangian for an O(N)-invariant scalar field theory is typically of the form

${\displaystyle {\mathcal {L}}={\frac {1}{2}}\eta ^{\mu \nu }\partial _{\mu }\phi \cdot \partial _{\nu }\phi -V(\phi \cdot \phi )}$

using an appropriate O(N)-invariant inner product. The theory can also be expressed for complex vector fields, i.e. for ${\displaystyle \phi \in \mathbb {C} ^{n}}$, in which case the symmetry group is the Lie group SU(N).

### Gauge-field couplings

When the scalar field theory is coupled to in a gauge invariant way to the Yang–Mills action, one obtains the Ginzburg–Landau theory of superconductors. The topological solitons of that theory correspond to vortices in a superconductor; the minimum of the Mexican hat potential corresponds to the order parameter of the superconductor.

## Quantum scalar field theory

A general reference for this section is Ramond, Pierre (2001-12-21). Field Theory: A Modern Primer (Second Edition). USA: Westview Press. ISBN 0-201-30450-3, Ch. 4

In quantum field theory, the fields, and all observables constructed from them, are replaced by quantum operators on a Hilbert space. This Hilbert space is built on a vacuum state, and dynamics are governed by a quantum Hamiltonian, a positive-definite operator which annihilates the vacuum. A construction of a quantum scalar field theory is detailed in the canonical quantization article, which relies on canonical commutation relations among the fields. Essentially, the infinity of classical oscillators repackaged in the scalar field as its (decoupled) normal modes, above, are now quantized in the standard manner, so the respective quantum operator field describes an infinity of quantum harmonic oscillators acting on a respective Fock space.

In brief, the basic variables are the quantum field φ and its canonical momentum π. Both these operator-valued fields are Hermitian. At spatial points x, y and at equal times, their canonical commutation relations are given by

{\displaystyle {\begin{aligned}\left[\phi \left({\vec {x}}\right),\phi \left({\vec {y}}\right)\right]=\left[\pi \left({\vec {x}}\right),\pi \left({\vec {y}}\right)\right]&=0,\\\left[\phi \left({\vec {x}}\right),\pi \left({\vec {y}}\right)\right]&=i\delta \left({\vec {x}}-{\vec {y}}\right),\end{aligned}}}

while the free Hamiltonian is, similarly to above,

${\displaystyle H=\int d^{3}x\left[{1 \over 2}\pi ^{2}+{1 \over 2}(\nabla \phi )^{2}+{m^{2} \over 2}\phi ^{2}\right].}$

A spatial Fourier transform leads to momentum space fields

{\displaystyle {\begin{aligned}{\widetilde {\phi }}({\vec {k}})&=\int d^{3}xe^{-i{\vec {k}}\cdot {\vec {x}}}\phi ({\vec {x}}),\\{\widetilde {\pi }}({\vec {k}})&=\int d^{3}xe^{-i{\vec {k}}\cdot {\vec {x}}}\pi ({\vec {x}})\end{aligned}}}

which resolve to annihilation and creation operators

{\displaystyle {\begin{aligned}a({\vec {k}})&=\left(E{\widetilde {\phi }}({\vec {k}})+i{\widetilde {\pi }}({\vec {k}})\right),\\a^{\dagger }({\vec {k}})&=\left(E{\widetilde {\phi }}({\vec {k}})-i{\widetilde {\pi }}({\vec {k}})\right),\end{aligned}}}

where ${\displaystyle E={\sqrt {k^{2}+m^{2}}}}$ .

These operators satisfy the commutation relations

{\displaystyle {\begin{aligned}\left[a({\vec {k}}_{1}),a({\vec {k}}_{2})\right]=\left[a^{\dagger }({\vec {k}}_{1}),a^{\dagger }({\vec {k}}_{2})\right]&=0,\\\left[a({\vec {k}}_{1}),a^{\dagger }({\vec {k}}_{2})\right]&=(2\pi )^{3}2E\delta ({\vec {k}}_{1}-{\vec {k}}_{2}).\end{aligned}}}

The state ${\displaystyle |0\rangle }$ annihilated by all of the operators a is identified as the bare vacuum, and a particle with momentum k is created by applying ${\displaystyle a^{\dagger }({\vec {k}})}$ to the vacuum.

Applying all possible combinations of creation operators to the vacuum constructs the relevant Hilbert space: This construction is called Fock space. The vacuum is annihilated by the Hamiltonian

${\displaystyle H=\int {d^{3}k \over (2\pi )^{3}}{\frac {1}{2}}a^{\dagger }({\vec {k}})a({\vec {k}}),}$

where the zero-point energy has been removed by Wick ordering. (See canonical quantization.)

Interactions can be included by adding an interaction Hamiltonian. For a φ4 theory, this corresponds to adding a Wick ordered term g:φ4:/4! to the Hamiltonian, and integrating over x. Scattering amplitudes may be calculated from this Hamiltonian in the interaction picture. These are constructed in perturbation theory by means of the Dyson series, which gives the time-ordered products, or n-particle Green's functions ${\displaystyle \langle 0|{\mathcal {T}}\{\phi (x_{1})\cdots \phi (x_{n})\}|0\rangle }$ as described in the Dyson series article. The Green's functions may also be obtained from a generating function that is constructed as a solution to the Schwinger–Dyson equation.

### Feynman path integral

The Feynman diagram expansion may be obtained also from the Feynman path integral formulation.[4] The time ordered vacuum expectation values of polynomials in φ, known as the n-particle Green's functions, are constructed by integrating over all possible fields, normalized by the vacuum expectation value with no external fields,

${\displaystyle \langle 0|{\mathcal {T}}\{\phi (x_{1})\cdots \phi (x_{n})\}|0\rangle ={\frac {\int {\mathcal {D}}\phi \phi (x_{1})\cdots \phi (x_{n})e^{i\int d^{4}x\left({1 \over 2}\partial ^{\mu }\phi \partial _{\mu }\phi -{m^{2} \over 2}\phi ^{2}-{g \over 4!}\phi ^{4}\right)}}{\int {\mathcal {D}}\phi e^{i\int d^{4}x\left({1 \over 2}\partial ^{\mu }\phi \partial _{\mu }\phi -{m^{2} \over 2}\phi ^{2}-{g \over 4!}\phi ^{4}\right)}}}.}$

All of these Green's functions may be obtained by expanding the exponential in J(x)φ(x) in the generating function

${\displaystyle Z[J]=\int {\mathcal {D}}\phi e^{i\int d^{4}x\left({1 \over 2}\partial ^{\mu }\phi \partial _{\mu }\phi -{m^{2} \over 2}\phi ^{2}-{g \over 4!}\phi ^{4}+J\phi \right)}=Z[0]\sum _{n=0}^{\infty }{\frac {i^{n}}{n!}}J(x_{1})\cdots J(x_{n})\langle 0|{\mathcal {T}}\{\phi (x_{1})\cdots \phi (x_{n})\}|0\rangle .}$

A Wick rotation may be applied to make time imaginary. Changing the signature to (++++) then turns the Feynman integral into a statistical mechanics partition function in Euclidean space,

${\displaystyle Z[J]=\int {\mathcal {D}}\phi e^{-\int d^{4}x\left[{1 \over 2}(\nabla \phi )^{2}+{m^{2} \over 2}\phi ^{2}+{g \over 4!}\phi ^{4}+J\phi \right]}.}$

Normally, this is applied to the scattering of particles with fixed momenta, in which case, a Fourier transform is useful, giving instead

${\displaystyle {\tilde {Z}}[{\tilde {J}}]=\int {\mathcal {D}}{\tilde {\phi }}e^{-\int {d^{4}p \over (2\pi )^{4}}\left({1 \over 2}(p^{2}+m^{2}){\tilde {\phi }}^{2}-{\tilde {J}}{\tilde {\phi }}+{g \over 4!}{\int {d^{4}p_{1} \over (2\pi )^{4}}{d^{4}p_{2} \over (2\pi )^{4}}{d^{4}p_{3} \over (2\pi )^{4}}\delta (p-p_{1}-p_{2}-p_{3}){\tilde {\phi }}(p){\tilde {\phi }}(p_{1}){\tilde {\phi }}(p_{2}){\tilde {\phi }}(p_{3})}\right)}.}$

where ${\displaystyle \delta (x)}$ is the Dirac delta function.

The standard trick to evaluate this functional integral is to write it as a product of exponential factors, schematically,

${\displaystyle {\tilde {Z}}[{\tilde {J}}]=\int {\mathcal {D}}{\tilde {\phi }}\prod _{p}\left[e^{-(p^{2}+m^{2}){\tilde {\phi }}^{2}/2}e^{-g/4!\int {d^{4}p_{1} \over (2\pi )^{4}}{d^{4}p_{2} \over (2\pi )^{4}}{d^{4}p_{3} \over (2\pi )^{4}}\delta (p-p_{1}-p_{2}-p_{3}){\tilde {\phi }}(p){\tilde {\phi }}(p_{1}){\tilde {\phi }}(p_{2}){\tilde {\phi }}(p_{3})}e^{{\tilde {J}}{\tilde {\phi }}}\right].}$

The second two exponential factors can be expanded as power series, and the combinatorics of this expansion can be represented graphically through Feynman diagrams of the Quartic interaction.

The integral with g = 0 can be treated as a product of infinitely many elementary Gaussian integrals: the result may be expressed as a sum of Feynman diagrams, calculated using the following Feynman rules:

• Each field (p) in the n-point Euclidean Green's function is represented by an external line (half-edge) in the graph, and associated with momentum p.
• Each vertex is represented by a factor −g.
• At a given order gk, all diagrams with n external lines and k vertices are constructed such that the momenta flowing into each vertex is zero. Each internal line is represented by a propagator 1/(q2 + m2), where q is the momentum flowing through that line.
• Any unconstrained momenta are integrated over all values.
• The result is divided by a symmetry factor, which is the number of ways the lines and vertices of the graph can be rearranged without changing its connectivity.
• Do not include graphs containing "vacuum bubbles", connected subgraphs with no external lines.

The last rule takes into account the effect of dividing by [0]. The Minkowski-space Feynman rules are similar, except that each vertex is represented by −ig, while each internal line is represented by a propagator i/(q2m2+), where the ε term represents the small Wick rotation needed to make the Minkowski-space Gaussian integral converge.

### Renormalization

The integrals over unconstrained momenta, called "loop integrals", in the Feynman graphs typically diverge. This is normally handled by renormalization, which is a procedure of adding divergent counter-terms to the Lagrangian in such a way that the diagrams constructed from the original Lagrangian and counter-terms is finite.[5] A renormalization scale must be introduced in the process, and the coupling constant and mass become dependent upon it.

The dependence of a coupling constant g on the scale λ is encoded by a beta function, β(g), defined by

${\displaystyle \beta (g)=\lambda \,{\frac {\partial g}{\partial \lambda }}~.}$

This dependence on the energy scale is known as "the running of the coupling parameter", and theory of this systematic scale-dependence in quantum field theory is described by the renormalization group.

Beta-functions are usually computed in an approximation scheme, most commonly perturbation theory, where one assumes that the coupling constant is small. One can then make an expansion in powers of the coupling parameters and truncate the higher-order terms (also known as higher loop contributions, due to the number of loops in the corresponding Feynman graphs).

The β-function at one loop (the first perturbative contribution) for the φ4 theory is

${\displaystyle \beta (g)={\frac {3}{16\pi ^{2}}}g^{2}+O\left(g^{3}\right)~.}$

The fact that the sign in front of the lowest-order term is positive suggests that the coupling constant increases with energy. If this behavior persisted at large couplings, this would indicate the presence of a Landau pole at finite energy, arising from quantum triviality. However, the question can only be answered non-perturbatively, since it involves strong coupling.

A quantum field theory is said to be trivial when the renormalized coupling, computed through its beta function, goes to zero when the ultraviolet cutoff is removed. Consequently, the propagator becomes that of a free particle and the field is no longer interacting.

For a φ4 interaction, Michael Aizenman proved that the theory is indeed trivial, for space-time dimension D ≥ 5.[6]

For D = 4, the triviality has yet to be proven rigorously, but lattice computations have provided strong evidence for this. This fact is important as quantum triviality can be used to bound or even predict parameters such as the Higgs boson mass. This can also lead to a predictable Higgs mass in asymptotic safety scenarios.[7]

## Notes

1. ^ i.e., it transforms under the trivial (0, 0)-representation of the Lorentz group, leaving the value of the field at any spacetime point unchanged, in contrast to a vector or tensor field, or more generally, spinor-tensors, whose components undergo a mix under Lorentz transformations. Since particle or field spin by definition is determined by the Lorentz representation under which it transforms, all scalar (and pseudoscalar) fields and particles have spin zero, and are as such bosonic by the spin statistics theorem. See Weinberg 1995, Chapter 5
2. ^ This means it is not invariant under parity transformations which invert the spatial directions, distinguishing it from a true scalar, which is parity-invariant.See Weinberg 1998, Chapter 19
3. ^ Brown, Lowell S. (1994). Quantum Field Theory. Cambridge University Press. ISBN 978-0-521-46946-3. Ch 3.
4. ^ A general reference for this section is Ramond, Pierre (2001-12-21). Field Theory: A Modern Primer (Second ed.). USA: Westview Press. ISBN 0-201-30450-3.
5. ^ See the previous reference, or for more detail, Itzykson, Zuber; Zuber, Jean-Bernard (2006-02-24). Quantum Field Theory. Dover. ISBN 0-07-032071-3.
6. ^ Aizenman, M. (1981). "Proof of the Triviality of ϕ4
d
Field Theory and Some Mean-Field Features of Ising Models for d > 4". Physical Review Letters. 47 (1): 1–4. Bibcode:1981PhRvL..47....1A. doi:10.1103/PhysRevLett.47.1.
7. ^ Callaway, D. J. E. (1988). "Triviality Pursuit: Can Elementary Scalar Particles Exist?". Physics Reports. 167 (5): 241–320. Bibcode:1988PhR...167..241C. doi:10.1016/0370-1573(88)90008-7.