Milwaukee Mandolin Orchestra. Photo courtesy of the Milwaukee Mandolin Orchestra.
(South Milwaukee, WI) – South Milwaukee Performing Arts Center is proud to present Music that Made Milwaukee Famous, featuring the Milwaukee Mandolin Orchestra with special guests Misha Litvin, Stas Venglevski and Robin Pluer on Saturday, January 26 at 7:30 pm.
The Milwaukee Mandolin Orchestra (MMO) has been a Milwaukee fixture since 1900. Known for its performance of music from America's golden age of mandolin orchestras (the late 1800s to early 1900s), the MMO is considered one of the best mandolin orchestras to perform rags, waltzes, and marches. Now with world renowned classical guitarists Rene Izquierdo and Elina Chekan as directors, the MMO captivates audiences with inspirational performances of preeminent works of the baroque and classical periods. Music that Made Milwaukee Famous will feature this unique combination of historic music. Join the MMO plus Milwaukee musicians Misha Litvin and Stas Venglevski, a fast fingered domra and bayan duo, and Robin Pluer, a lovely and charming chanteuse.
"While we've known about the MMO for some time, we knew the time was right to feature them on our stage when we learned that one of our long-time volunteers was a member," explains Rachel Sorce, Executive Director. The volunteer is Diane Pautzke, who along with her husband Dale, are frequent ushers or docents at South Milwaukee Performing Arts Center. "The Pautzke's have an inspiring passion and joy the arts and life. We're lucky to have them as volunteers," adds Sorce.
Stas Venglevski. Photo courtesy of the South Milwaukee Performing Arts Center.
His artistry, dazzling technical command, and sensitivity have brought Stanislav, "Stas," Venglevski, a native of the Republic of Moldova, part of the former Soviet Union, increasing acclaim as a virtuoso of the Bayan. A two-time first prize winner of Bayan competition in the Republic of Moldova, Stas is a graduate of the Russian Academy of Music in Moscow where he received his Masters Degree in Music under the tutelage of the famed Russian Bayanist, Friedrich Lips. In 1992 he immigrated to the United States.
Stas is an accordionist, a musician, an arranger, an entertainer and a teacher. Stas' repertoire includes his original compositions, a broad range of classical, contemporary and ethnic music. He has toured extensively as a soloist throughout the former Soviet Union, Canada, Europe, and the United States, including numerous performances with Doc Severinsen, Steve Allen and Garrison Keillor on the Prairie Home Companion. Additionally, he has performed with symphony orchestras throughout the United States. He performed the world premiere of Concerto No. 2 by Anthony Galla-Rini and also the world premiere of Bayan and Beyond, composed for Stas by Dan Lawitts.
He is a regular participant the Milwaukee Symphony Orchestra's Arts in Community Education Program (ACE); has performed with the Chicago Symphony Orchestra and the Tacoma Symphony Orchestra; has done television commercials and performed in theater productions; produced 15 acclaimed albums including a transcription of Tchaikovsky's Nutcracker Suite for bayan as well as one of original compositions. He has published several books of original compositions.
Stas founded Accordion XXI Century Series in 2010 so that Midwest audiences could experience the amazing range of the accordion and bayan by bringing gifted artists from all over the world. In a concert setting, these gifted musicians share their skills and cultures to provide the audience with a unique musical experience. The performances feature the accordion or bayan in solo presentation and, when possible, in concert with other instruments.
Tickets: Adult $20-30 with discounts for seniors and students. Tickets may be purchased online at www.southmilwaukeepac.org or through our box office at 414-766-5049 or in person at 901 15th Avenue. Box office hours are M-F (by phone 10-4 and walk-up 10-1). If purchasing in person, ring bell at door #7 and show ID. Sales at the door open one hour before the show, while tickets last.
South Milwaukee Performing Arts Center (SMPAC) provides the greater Milwaukee and southeastern Wisconsin communities with creative, innovative and diverse performing arts. Located inside of the South Milwaukee School District's 6-12 campus, it serves students of South Milwaukee and provides professional services for more than 500 performances, rehearsals, classes and other events annually.
Past performances on our stage include the Soweto Gospel Choir, Big Bad Voodoo Daddy, The Vienna Boys Choir, Flamenco Vivo Carlotta Santana, The Violent Femmes, Tommy Emmanuel, Legends Roundtable to Honor "Da Crusher," Ex Fabula, Cirque Alfonse, The Official Blues Brothers Revue, John McGivern, George Watsky, Donny McCaslin, Robert Glasper, The Zombies, Jean Luc Ponty, Jon Anderson and many, many more.
SMPAC was voted as a top five Best Theatre in City Voter's Milwaukee A-List Best Of contest in 2016 and 2017, receiving customer reviews such as "Great venue with fabulous events for all ages!" "Excellent and diverse touring artist performances showcased in a comfortable, friendly theatre away from the downtown crowds." "There is not a bad seat in the house." SMPAC was named the tri-city South Shore Chamber of Commerce Outstanding Business Award for 2017.
SMPAC's annual Performing Arts Series is sponsored in part by the Classic Cargo International Inc., Courtyard Marriott Milwaukee Airport, Skyline Catering & Express Deli, TASC Services LLC., and Ken Cook Co. Performances are supported in part by a grant from the Wisconsin Arts Board with funds from the State of WI and the National Endowment for the Arts.
SMPAC is located inside of the South Milwaukee School District's 6-12 campus, at 901 15th Avenue in South Milwaukee between College and Rawson Avenues. It is easily accessible from I-94 and 794. Free parking is available in the northwest parking lot. For events, patrons should enter door #9. For tickets or more information, visit southmilwaukeepac.org or call (414) 766-5049.


text:
Maker Faire Celebrates Do-It-Yourself-Culture
By Stan Alcorn
Thousands of people gathered at the New York Hall of Science this weekend for what's called the World Maker Faire. It was the third an annual celebration of 21st century Do-It-Yourself culture, with workshops, speakers and demonstrations.
But, as reporter Stan Alcorn discovered, the main attraction is the makers themselves.
STAN ALCORN, BYLINE: At the center of the World Maker Faire is Katy Perry.
JESSE GREEN: Katy Perry is the unicorn that we made for a friend's wedding.
ALCORN: This standard carousel horse was named after the singer after being modified by Jesse Green.
GREEN: She sneezes glitter and she shoots colored methanol fire out of her horn.
(SOUNDBITE OF BLAST)
CHRIS ANDERSON: Flame shooting is a long Maker Faire tradition.
ALCORN: Chris Anderson's new book "Makers" comes out Tuesday. He thinks we shouldn't let the bright green flames blind us to a broader Maker Movement, which is leading everyone become a manufacturer the same way that the Web let everyone be a publisher.
ANDERSON: You know, the Web has got, you know, cat videos and it's got Facebook. The point is that there's room for everybody.
ALCORN: There does seem to be room for everybody at Maker Faire. There's a race track for electric cars, classes in lock picking and crochet; there's even a trapeze for circus acrobats. But what connects them all? I asked Maker Faire founder Dale Dougherty.
DALE DOUGHERTY: I think it's sort of this notion of participatory culture where we do things, we make things. You know, we're not just consumers, we're producers.
ALCORN: Producers with an increasingly sophisticated set of tools.
DOUGHERTY: There's kind of a burgeoning democratization of technology where things that only professionals use are now accessible and affordable for amateurs.
ALCORN: For instance, infrared sensors. By hiding 12 of them in a fish tank, and programming each one to play a different tone when a fish swims by, Chris Losee and his daughter Jules created the Musiquarium.
JULES LOSEE: Last year, we did an instrument called the Slugophone. And it was basically the same thing, except it involved caterpillars.
ALCORN: There are more utilitarian makers here too. Andy Wekin is a mechanical engineer who consults with farms. He's showing a steady stream of kids what it feels like to generate 100 watts of power on a bicycle.
ANDY WEKIN: So that's like a television right there, you're pedaling the television.
UNIDENTIFIED CHILD: Daddy, listen (unintelligible).
ALCORN: His Pedal Power project is meant to be practical; powering a water pump for a rooftop farm in Brooklyn, for instance. But he likes that people here also see it as art.
WEKIN: I really do see the art and the maker and the do-it-yourself and the inventor as all part of a spectrum. It's fun to have that interplay.
ALCORN: Kim Holleman is from the art side of the spectrum. She's here presenting Trailer Park, a working ecosystem housed in an 18-foot silver trailer. At galleries, people ask her abstract questions, but at Maker Faire...
KIM HOLLEMAN: I've already like described drip irrigation system, the construction of the planter beds, what size the brick is.
ALCORN: Not that Holleman minds.
HOLLEMAN: People have already asked me if they could take this idea, and I've already told them, like I'm going to take yours. You better take mine.
ALCORN: Holleman calls it open source art. Or you could just call its sharing.
For NPR News, I'm Stan Alcorn in New York. Transcript provided by NPR, Copyright NPR.
NPR National News
Stan Alcorn

redpajama_set_name: RedPajamaCommonCrawl


I started thinking about our survival needs, from what came the important question: why are we not more careful on what we do on the planet, when it is what offer us the possibility to live?
Our body is composed between 60% and 80% of water. It (water) provides the environment necessary for life.
A sandglass is meant to give the time like it is indefinite, but what if it was leaking ?
I am thinking to make one with water. The amount of water inside would be equivalent on the volume available on earth/per person, and would leak in accordance of the diminishing of the resource.


text:
Q: Adding image to login page in cakephp I'm creating a login page in cakephp. Instead of writing "Login", I thought of showing an image. This is how I tried:

        <?= $this->Form->create(); ?>
            <?= $this->Form->input('email'); ?>
            <?= $this->Form->input('password', array('type' => 'password')); ?>
            <?= $this->Form->submit('Login', array('class' => 'button')); ?>
        <?= $this->Form->end(); ?>

In the above layout, I tried to add a image logo.png instead of showing "Login". But, the image did not load. I've placed the image in webroot/img/logo.png. But, the image is not loading. What's wrong with this? What should I change or add?

A: You should refer to the document: HtmlHelper::image
Try this:

  <?php echo $this->Html->image('logo.png'); ?>

A: change the src to use logo.png instead of cake.icon.png

redpajama_set_name: RedPajamaStackExchange


MennoNerds is a network of Anabaptists from around the Internet interacting through a variety of media. What is a MennoNerd? It doesn't necessarily mean "Menno", with Anabaptists of all varieties welcome. It also doesn't necessarily mean nerdy in the stereotypical sense, although that applies for many of us. Admittedly, the name is more for fun than it is descriptive.
We will be a "go to" place for people to hear what Anabaptists have to say about following Jesus in a variety of contexts and topics, with a recognition and reverence of the wide diversity of race/ethnicity, gender, generation, sexuality, ability, and theology found in the Anabaptist stream.
Somewhere in the fall of 2012, a tweet was sent out into the blackness of the interwebs by a lonely nerdy Mennonite named Chris Lenshyn. It included the hashtag, #MennoNerd. Starting with that one little hashtag, suddenly Anabaptist tweeps started popping up and connecting with each other, along with their blogs, all over the 'Net.
Putting our nerdy heads together and pooling resource of hardware, time, know-how, and nerd-powers, we put together this website. From there, momentum kept building as we've continued to grow and evolve into what we are today.
Meet our mascot, Rebstock NerdBird! You'll see this image pretty much everywhere MennoNerds hang out as we love our little birdy.
Why Rebstock? In September, 2013, we had a contest to name our bird. A lot of excellent names were suggested but, at the end, Rebstock won out. The person who nominated Rebstock, Tim Nafziger, wrote the following about his choice.
This is the last name of Barbara Rebstock, a woman who is not talked about very much today, but who was a major Anabaptist prophet in Strasbourg. She was willing to stand up to David Joris, a misogynist Anabaptist leader who tried to shame the Anabaptist men she worked with[, calling them] weak because they let her lead.
Also: I like the sound of Rebstock as a word. It's rhythmic and has arcane echoes of the word rebel in a provocative way.
So, not only is this truly a MennoNerd bird (who else but MennoNerds would know about Barbara Rebstock), but the representative history of the name reflects who we are.
MennoNerds Name by Chris Lenshyn on behalf of the MennoNerds community is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
All MennoNerds Logos of Rebstock Nerdbird by Eddie Gonzalez on behalf of the MennoNerds community are licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.


text:
const { mix } = require('laravel-mix');

/*
 |--------------------------------------------------------------------------
 | Mix Asset Management
 |--------------------------------------------------------------------------
 |
 | Mix provides a clean, fluent API for defining some Webpack build steps
 | for your Laravel application. By default, we are compiling the Sass
 | file for the application as well as bundling up all the JS files.
 |
 */

mix.scripts([
        'resources/assets/js/stickyfooter.js',
        'resources/assets/js/slider.js',
        'resources/assets/js/togglewindow.js',
        'resources/assets/js/captcha.js',
    ], 'resources/assets/js/app.js')
    .js('resources/assets/js/app.js', 'public/js')
    .sass('resources/assets/sass/app.sass', 'public/css');

redpajama_set_name: RedPajamaGithub


text:
Home / Photos and Videos
Photos: Coe College vs. Cornell Women's Basketball
Cornell forward Rachael Adewusi (25) reaches up and fouls on Coe College center Kaalyn Petersen (33) as she shoots the ball in the first half of the game at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
Cornell forward Ilah Perez-Johnson (32) puts her hands up to block the shot made by Coe College guard Ellie Wisner (22) in the first half of the game at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
Cornell center Madison Wauters (44) pushes past Coe College center Kaalyn Petersen (33) as she tries to block her shot in the first half of the game at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
Cornell forward Rachael Adewusi (25) puts her hands up to block Coe College center Kaalyn Petersen (33) as she looks to shoot the ball in the first half of the game at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
Coe College forward Macey Rogers (3) and guard Elle Walker (4) block Cornell guard Megan Gandrup (14) as she looks to pass the ball in the first half of the game at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
Coe College guard Katie Wilhelmi (24) guards Cornell Victoria Saucedo (15) as she drives the ball down the court in the first half of the game at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
Cornell forward Ilah Perez-Johnson (32) reaches over and blocks the ball as Coe College guard Molly Buck (5) shoots the ball in the first half of the game at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
Coe College guard Ella Imler (15) tries to block Cornell guard Madison Osborn (5) as she drives the ball towards the net and shoots the ball in the first half of the game at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
Cornell forward Rachael Adewusi (25) jumps up to grab control of the rebound, but loses control as Coe College center Kaalyn Petersen (33) grabs the ball in the first half of the game at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
Cornell forward Ilah Perez-Johnson (32) shoots the ball and gets two-points for the Rams in the first half of the game at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
Cornell women's basketball Head Coach Brent Brace reacts to a call made by the refs in the fourth quarter of the game at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
The Cornell bench reacts after their team scored a two-pointer in the fourth quarter of the game against Coe College at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021. (Savannah Blake/The Gazette)
Coe College fell to Cornell at Coe College in Cedar Rapids, Iowa on Wednesday, Dec. 15, 2021.
Coe Kohawks, Cornell Rams
Photojournalist, The Gazette
Photojournalist. View our Photos and Videos page
Photos: J-Hawk Invitational wrestling
Photos: Iowa vs. Indiana Men's Basketball
Photos: North Linn at Springville boys' basketball
Photos: North Linn at Springville girls' basketball
All articles by Savannah
Coe men's basketball looking for another hot streak
Justin Webster Sports Jan. 14, 2022 1:27 pm
Photos: Coe men's basketball vs. Dubuque
Gazette Visuals Jan. 5, 2022 10:36 pm
Photos: Coe women's basketball vs. Dubuque
Photos: Solon high school girls wrestling invitational
Jan. 17, 2022 6:31 pm
Photos: Big Ten Wrestling--#15 Purdue at #1 Iowa
Jan. 9, 2022 4:44 pm
Photos: Pick-up pond hockey in Coralville
Photos: Iowa wrestling vs. Minnesota
Jan. 7, 2022 11:32 pm


text:
TechRadar survey shows rise of the machines is not there yet
By Desire Athow
No surprise whatsoever
There's more smartphones in the UK than there are inhabitants so it shouldn't come as a surprise that the overwhelming majority of us carry or interact with one or more electronic devices.
A TechRadar survey shows that most of our readers (nearly 90%) use three or more electronic devices on any given day with four being the average.
Electronic devices for the purpose of the survey included smartphones, tablets, wearables and any personal piece of electronics that a consumer would use.
Four doesn't seem an incredibly large number given how gadgets have taken over lives and it is likely that this number will go up given the rising popularity of wearables.
More than four and a half thousands TechRadar readers have participated in that survey.
The question for that survey was suggested by Lenovo's CTO, Peter Hortenius, during a recent interview.
This survey was carried out in the wake of the launch of Windows 10 which happened last week. You can read our Windows 10 review and our ongoing coverage of Windows 10.
Check out the results of our previous surveys:
Two-thirds of our readers plan to upgrade to Windows 10 in 2015
Use antivirus? Our research shows you probably update it manually
TechRadar readers are jumping on Windows 10 bandwagon
TechRadar survey shows you don't want Windows 10 unless it's cheap
Slow PC? TechRadar survey shows one third would blame antivirus
And there's still time to vote in our currently running survey:
Do you plan to buy a new computer (laptop, desktop, tablet) to run Windows 10?
Which of these features made you upgrade to Windows 10?
Desire Athow
Managing Editor, TechRadar Pro
Désiré has been musing and writing about technology during a career spanning four decades. He dabbled in website builders and web hosting when DHTML and frames were in vogue and started narrating about the impact of technology on society just before the start of the Y2K hysteria at the turn of the last millennium.
See more PC news
I love the new MacBooks, but they badly need a dash of iBook color
I can't believe Age of Empires 2 is playable in a browser
Age of Empires 2 arriva su Cloud: ritorna un classico intramontabile


text:
Comic Creator Bill Wright
Bill Wright
(4 October 1917 - 12 June 1984, USA)
'Mickey Mouse'.
William George Wright was a comic artist for Disney, who drew many of the 'Mickey Mouse' stories. Wright got his education at the Los Angeles Art Center and the Los Angeles Technical Trade Institute. He joined the Disney Studios in 1937. A year later, he was assigned by the Comic Strip Department to assist Ted Thwaites on inking Floyd Gottfredson's 'Mickey Mouse' stories.
Thwaites left Disney in 1940 and for years Wright was one of the main inkers on the daily and Sunday 'Mickey Mouse' pages. From 1943 he also started to do pencilling on the Mickey Sunday pages. Bill Wright continued working for Disney until his death in 1984, drawing daily pages with such characters as 'Scamp', 'Br'er Rabbit' and, of course, 'Mickey Mouse'.
Inducks entry
Artwork © 1984 Bill Wright
Series and books by Bill Wright you can order today:


Observations and art news by the members of New England Wax, professional artists who paint with the ancient medium of Encaustic.
New England Wax is an organization of professional artists based in the New England states of the United States. All N.E.W. artists utilize the medium of encaustic (the use of beeswax mixed with tree resin and/or pigments) in their art. Members meet regularly to organize group exhibitions and to share their knowledge with each other. This blog is a collaboration by N.E.W. members about the world of art and the influence it has on their work. For more information on New England Wax and for member profiles visit our website at http://www.newenglandwax.org.


text:
\section{Introduction}

Using the Clifford and spin Clifford bundle formalisms and some few results of
the theory of extensor calculus we derive the conservation laws for the
probability current, energy-momentum and total angular momentum
\emph{extensor} \emph{fields} resulting from the structure of Dirac-Hestenes
\ equation (DHE) satisfied by a Dirac-Hestenes spinor field (DHSF) in
interaction with an electromagnetic field \ without using the Lagrangian
formalism\footnote{We recall that the concepts of multiform functions and
extensor fields permit us to give a nice Lagrangian (and Hamiltonian)
formalism for all relativistic fields and in particular to derive the
conserved energy-momentum, spin and angular momentum extensor fields for
interacting relativistic fields. Preliminary details of our formalism has been
first presented in \cite{rsv1993,m1999,mfr2001,} and further elaborated in
\cite{rc2007}.}. We show in a quite simple way that the energy-momentum
extensor field\footnote{Related to theTetrode tensor of the Dirac spinor
field.} of the DHSF is not symmetric and that its antisymmetric part is the
\emph{source }of the \emph{spin extensor field} of the free DHSF. Moreover we
show that the conservation laws for the energy-momentum and total angular
momentum extensor for the coupled system of the DHSF and the electromagnetic
field is very different from what is expected from a classical point of view.
In particular these laws show in an elegant way that in spacetime regions with
topology permitting the existence of an electromagnetic field potential
$A\neq0$ but with $F=0$ the energy-momentum and total angular momentum of the
sole DHSF are not conserved. This is clearly according to our view the origin
of the Bohm-Aharonov effect.

In Section 3 we briefly recall results obtained in \cite{rw2016a} where it was
shown that (a): that the classical\ relativistic Hamilton-Jacobi equation
(HJE) \ for a charged electrical particle in interaction with the
electromagnetic field is equivalent to a DHE satisfied by a special class of
DHSF that we call \emph{classical }DHSF which are characterized by having the
Takabayashi angle equal to $0$ or $\pi$ and moreover that the DHE satisfied by
a classical DHSF is equivalent to the HJE; (b) The identification of the
correct relativistic quantum potential resulting from the DHE in a de
Broglie-Bohm approach leading to a HJE like equation for the motion of
(spinning) charged particle.

Equipped with these results and the ones of Section 2 we analyze in Section 3
results of \cite{hc1,hc2} were authors though that they have disclosed the
relativistic quantum potential for the Dirac particle. We prove that the
results of those papers are equivocated by explicitly showing with detailed
calculations were authors get mislead.

In Section 4 we present our conclusions and in the Appendix we recall the
notation and some results of the Clifford and spin-Clifford bundles formalism
used in the paper.

\section{Dirac-Hestenes Equation (DHE) and Conserved Currents}

With the notations introduced in the Appendix the DHE for $\phi_{L}$ $\in
\sec\mathcal{C\ell}^{0}(M,\mathtt{\eta})$ \ and $\phi_{R}$ $\in\sec
\mathcal{C\ell}^{0}(M,\mathtt{\eta})$ \ in the presence of an electromagnetic
potential $A\i
{\textstyle\bigwedge\nolimits^{1}}
T^{\ast}M$ $\hookrightarrow\sec\mathcal{C\ell}^{0}(M,\mathtt{\eta})$ are
\begin{align}
\boldsymbol{\partial}\phi_{L}\gamma_{21}-eA\phi_{L}-m\phi_{L}\gamma_{0}  &
=0,\label{1}\\
\gamma_{12}\phi_{R}\overleftarrow{\boldsymbol{\partial}}-e\phi_{R
A-m\gamma_{0}\phi_{R}  &  =0 \label{1A
\end{align}
Multiplying Eq.(\ref{1}) on the right by $\gamma_{0}$ $\phi_{R}$we ge
\begin{equation}
\boldsymbol{\partial}\phi_{L}\gamma_{012}\phi_{R}-eA\phi_{L}\gamma_{0}\phi
_{R}-m\phi_{L}\phi_{R}=0 \label{2
\end{equation}

Now, taking notice that for any odd $O\in\sec$ (
{\textstyle\bigwedge\nolimits^{1}}
T^{\ast}M
{\textstyle\bigwedge\nolimits^{3}}
T^{\ast}M$)$\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta})$ it i
\begin{equation}
\langle O\rangle_{1}=\frac{1}{2}(O+\tilde{O}) \label{3
\end{equation}
and tha
\begin{equation}
\partial_{\mu}(\phi_{L}\gamma_{012}\phi_{R})=\partial_{\mu}\phi_{L
\gamma_{012}\phi_{R}+\phi_{L}\gamma_{012}\partial_{\mu}\phi_{R}, \label{4
\end{equation}
we hav
\begin{equation}
\langle\partial_{\mu}\phi_{L}\gamma_{012}\phi_{R}\rangle_{1}=\frac{1
{2}\left(  \partial_{\mu}\phi_{L}\gamma_{012}\phi_{R}-\phi_{L}\gamma
_{012}\partial_{\mu}\phi_{R}\right)  . \label{5
\end{equation}
Summing Eq.(\ref{4}) (multiplied by $1/2)$ with Eq.(\ref{5}) and multiplying
on the left by $\gamma^{\mu}$ we get
\begin{equation}
\frac{1}{2}\boldsymbol{\partial}(\phi_{L}\gamma_{012}\phi_{R})+\gamma^{\mu
}\langle\partial_{\mu}\phi_{L}\gamma_{012}\phi_{R}\rangle_{1
=\boldsymbol{\partial}\phi_{L}\gamma_{012}\phi_{R}. \label{6
\end{equation}
Next, using Eq.(\ref{1}) on the right side of Eq.(\ref{3}) we ge
\begin{equation}
\frac{1}{2}\boldsymbol{\partial}(\gamma_{5}s)+\gamma^{\mu}\langle\partial
_{\mu}\phi_{L}\gamma_{012}\phi_{R}\rangle_{1}=eAJ+m\phi_{L}\phi_{R} \label{7
\end{equation}
where
\begin{equation}
s=\phi_{L}\gamma^{3}\phi_{R}\text{ ~and ~}J=\phi_{L}\gamma^{0}\phi_{R}
\label{8
\end{equation}
are bilinear invariants of Dirac theory called respectively the spin $1$-form
field and the probability current $1$-form field.\footnote{Details in
\cite{rc2007}.}

\subsection{The Conserved Probability Current}

From Eq.(\ref{1}) we also hav
\begin{equation}
\boldsymbol{\partial}\phi_{L}\gamma_{0}\phi_{R}=eA\phi_{L}\gamma_{012}\phi
_{R}+m\phi_{L}\gamma_{21} \label{1c
\end{equation}

Now, taking also into account that for $O\in\sec$ (
{\textstyle\bigwedge\nolimits^{1}}
T^{\ast}M
{\textstyle\bigwedge\nolimits^{3}}
T^{\ast}M$)$\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta})$ it is
\begin{equation}
\langle O\rangle_{3}=\frac{1}{2}(O-\tilde{O}) \label{9
\end{equation}
we also have the identitie
\begin{align}
\partial_{\mu}(\phi_{L}\gamma_{0}\phi_{R})  &  =\partial_{\mu}\phi_{L
\gamma_{0}\phi_{R}+\phi_{L}\gamma_{0}\partial_{\mu}\phi_{R},\label{10}\\
\langle\partial_{\mu}\phi_{L}\gamma_{0}\phi_{R}\rangle_{3}  &  =\frac{1
{2}\left(  \partial_{\mu}\phi_{L}\gamma_{0}\phi_{R}-\phi_{L}\gamma_{0
\partial_{\mu}\phi_{R}\right)  \label{10a
\end{align}
and summing Eqs.(\ref{10}) and (\ref{10a}) and multiplying on the left by
$\gamma^{\mu}$ we ge
\begin{equation}
\frac{1}{2}\boldsymbol{\partial}(\phi_{L}\gamma_{0}\phi_{R})+\gamma^{\mu
}\langle\partial_{\mu}\phi_{L}\gamma_{0}\phi_{R}\rangle_{3
=\boldsymbol{\partial}\phi_{L}\gamma_{0}\phi_{R} \label{11
\end{equation}
Using Eq.(\ref{1c}) in Eq.(\ref{11}) we get \
\begin{equation}
\boldsymbol{\partial}J+\gamma^{\mu}\langle\partial_{\mu}\phi_{L}\gamma_{0
\phi_{R}\rangle_{3}=-eA\gamma_{5}s. \label{12
\end{equation}
Now, from Eq.(\ref{12}) we get
\begin{align}
\langle\boldsymbol{\partial}J+\gamma^{\mu}\langle\partial_{\mu}\phi_{L
\gamma_{0}\phi_{R}\rangle_{3}\rangle_{0}  &  =\langle\boldsymbol{\partial
}J\rangle_{0}=\boldsymbol{\partial\lrcorner}J,\nonumber\\
\langle-eA\gamma_{5}s\rangle_{0}  &  =-e\langle\langle A\gamma_{5}s\rangle
_{2}+\langle A\gamma_{5}s\rangle_{2}\rangle_{0}=0 \label{13
\end{align}
and finally we have the conservation law for the probability
current\footnote{Recall that $\boldsymbol{\partial}=d-\delta$, where
$d=\boldsymbol{\partial\wedge}$ is the differential operator and
$\delta=-\boldsymbol{\partial}\boldsymbol{\lrcorner}$ is Hodge codifferential
operator}, i.e.,
\begin{equation}
\boldsymbol{\partial\lrcorner}J=-\delta J=0. \label{14
\end{equation}

\section{The Energy-Momentum Extensor of the Dirac-Hestenes Field}

Recalling that for $v\in\sec$
{\textstyle\bigwedge\nolimits^{1}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta})$ and
$\mathcal{C\in}\sec\mathcal{C\ell}(M,\mathtt{\eta})$ the following identity
holds \cite{rc2007}
\begin{equation}
\boldsymbol{\partial}(v\mathcal{C})=\boldsymbol{\partial}(v)\mathcal{C-
v(\boldsymbol{\partial}\mathcal{C})+2(v\lrcorner\boldsymbol{\partial
)}\mathcal{C} \label{16
\end{equation}
we immediately get from Eq.(\ref{1}) after some trivial algebra that
\begin{equation}
\boldsymbol{\partial}^{2}\phi_{L}=(e^{2}A^{2}-m^{2})\phi_{L
-e[(\boldsymbol{\partial}A)\phi_{L}+2(A\lrcorner\boldsymbol{\partial)}\phi
_{L}]\gamma_{21}. \label{15
\end{equation}
Next, recalling again the identity given by Eq.(\ref{3}) we have
\begin{equation}
\langle\boldsymbol{\partial}^{2}\phi_{L}\gamma_{012}\phi_{R}\rangle_{1
=\frac{1}{2}\left(  \boldsymbol{\partial}^{2}\phi_{L}\gamma_{012}\phi_{R
-\phi_{L}\gamma_{012}\boldsymbol{\partial}^{2}\phi_{R}\right)  . \label{17
\end{equation}
Next, using Eq.(\ref{17}) on the right side of Eq.(\ref{15}) multiplied by
$\gamma_{012}\phi_{R}$\ we ge
\begin{equation}
\langle\boldsymbol{\partial}^{2}\phi_{L}\gamma_{012}\phi_{R}\rangle
_{1}=eF\llcorner J+e[(\boldsymbol{\partial\lrcorner}A)J+(A\lrcorner
\boldsymbol{\partial})J] \label{18
\end{equation}
with $F=\boldsymbol{\partial}\wedge A=dA\in\sec$
{\textstyle\bigwedge\nolimits^{2}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta})$ is the Faraday field.

We now write Eq.(\ref{18}) in a convenient form which permit us to introduce
the energy-momentum $(1,1)$-extensor field for the Dirac-Hestenes field, i.e.,
the objec
\begin{align}
\boldsymbol{T}  &  :\se
{\textstyle\bigwedge\nolimits^{1}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta})\rightarrow\se
{\textstyle\bigwedge\nolimits^{1}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta}),\nonumber\\
n  &  \mapsto\boldsymbol{T}(n) \label{19
\end{align}
such that
\begin{equation}
\boldsymbol{T}(\gamma^{\mu})\cdot\gamma^{\nu}=T^{\mu\nu} \label{20
\end{equation}
are the components of the energy-momentum tensor of the Dirac field. In order
to proceed we introduce the differential operators
\begin{equation}
\boldsymbol{\partial}_{n}:=\gamma^{\mu}\frac{\partial}{\partial n^{\mu}}\text{
~and ~}\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial}=\eta^{\mu\nu
\frac{\partial}{\partial n^{\mu}}\frac{\partial}{\partial\mathrm{x}^{\nu}}
\label{21
\end{equation}
acting on the bundle of the $(1,1)$-extensor fields. Recalling moreover that
for any $\mathcal{C\in}\sec\mathcal{C\ell}(M,\mathtt{\eta})$ it i
\begin{equation}
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial(}n\cdot\partial
\mathcal{C)}=\boldsymbol{\partial}^{2}\mathcal{C} \label{22
\end{equation}
and
\begin{equation}
\partial^{\mu}\mathcal{C}=\gamma^{\mu}\cdot\boldsymbol{\partial
_{n}\boldsymbol{(}n\cdot\partial\mathcal{C)} \label{23
\end{equation}
the left side of Eq.(\ref{18}) can be written a
\begin{equation}
\langle\boldsymbol{\partial}^{2}\phi_{L}\gamma_{012}\phi_{R}\rangle
_{1}=\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial}\langle(n\cdot
\boldsymbol{\partial)}\phi_{L}\gamma_{012}\phi_{R}\rangle_{1}. \label{24
\end{equation}
Now, observe that it is
\begin{align}
(\boldsymbol{\partial\lrcorner}A)J+(A\lrcorner\boldsymbol{\partial})J  &
=\gamma^{\mu}\cdot(\boldsymbol{\partial}_{\mu}A)J+\gamma^{\mu}\cdot
A\boldsymbol{\partial}_{\mu}J\nonumber\\
&  =\gamma^{\mu}\cdot\boldsymbol{\partial}_{n}[(\partial_{\mu}n)\cdot
AJ+n\cdot(\partial_{\mu}A)J+n\cdot A\partial_{\mu}J]\nonumber\\
&  =\gamma^{\mu}\cdot\boldsymbol{\partial}_{n}\partial_{\mu}(n\cdot
AJ)\nonumber\\
&  =\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial(}n\cdot
AJ\boldsymbol{).} \label{25
\end{align}
Then, using Eqs.(\ref{24}) and (\ref{25}) we can write Eq.(\ref{18})
as\footnote{Recall that classicaly $eF\lrcorner J$ represents the Lorentz
force law.
\begin{equation}
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial\lbrack}\langle
(n\cdot\boldsymbol{\partial)}\phi_{L}\gamma_{012}\phi_{R}\rangle_{1}-en\cdot
AJ]=eF\lrcorner J. \label{26
\end{equation}
We now write
\begin{equation}
\boldsymbol{T}^{\dagger}(n):=\langle(n\cdot\boldsymbol{\partial)}\phi
_{L}\gamma_{012}\phi_{R}\rangle_{1}-en\cdot AJ \label{28
\end{equation}
where $\boldsymbol{T}^{\dagger}$ denotes the adjoint of a $(1,1)$-extensor
field $\boldsymbol{T}$, i.e., for $n,m\in\se
{\textstyle\bigwedge\nolimits^{1}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta})$ it is
\begin{equation}
\boldsymbol{T}(n)\cdot m=n\cdot\boldsymbol{T}^{\dagger}(m) \label{27
\end{equation}
and write Eq.(\ref{26}) a
\begin{equation}
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial T}^{\dagger}(n)=eF\lrcorner
J \label{29
\end{equation}
which can also be written a
\[
\boldsymbol{\partial\cdot T}^{\dagger}(\gamma_{\mu})=e(F\lrcorner
J)\cdot\gamma_{\mu
\]

When $A=0$ we write $\boldsymbol{T}^{\dagger}(n)=\boldsymbol{T}_{D}^{\dagger
}(n)$
\begin{equation}
\boldsymbol{T}_{D}^{\dagger}(n)=\langle(n\cdot\boldsymbol{\partial)}\phi
_{L}\gamma_{012}\phi_{R}\rangle_{1} \label{30
\end{equation}
which is the energy-momentum extensor field of the Dirac-Hestenes field.
Obviously, in a region where $\ F=0$ and $A=0$, $\boldsymbol{T}_{D}^{\dagger
}(n)$ is conserved, i.e.,
\begin{equation}
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial T}_{D}^{\dagger}(n)=0.
\label{31
\end{equation}
We write
\begin{equation}
\boldsymbol{T}^{\mu}=\boldsymbol{T}(\gamma^{\mu}):=T^{\mu\nu}\gamma_{\nu}
\label{32
\end{equation}
and of cours
\begin{equation}
\boldsymbol{T}^{\dagger\mu}=\boldsymbol{T}^{\dagger}(\gamma^{\mu})=T^{\nu\mu
}\gamma_{\nu}. \label{33
\end{equation}
The objects $\boldsymbol{T}^{\mu}\in\se
{\textstyle\bigwedge\nolimits^{1}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta})$are said to be
the energy-momentum 1-form fields of the Dirac field in interaction with an
electromagnetic field. The $T^{\mu\nu}$ are the components of the so-called
Tetrode energy-momentum tensor of the Dirac field and as it is well known and
will be shown below it i
\begin{equation}
T^{\mu\nu}\neq T^{\nu\mu}, \label{34
\end{equation}
i.e., the Tetrode tensor is not symmetric, something that has a nontrivial
implication shown in subsection \ref{sourcesp}, namely that the antisymmetric
part of the energy-momentum tensor is the source of the spin field of the
Dirac field.

\subsection{The Trace and the Bif of the Extensor field $\boldsymbol{T}$}

To proceed, we need some results, in particular the \emph{trace} \ and the
\emph{bif} of the extensor field $\boldsymbol{T}$ defined \cite{rc2007}
respectively by b
\begin{align}
\mathrm{tr}(\boldsymbol{T})  &  =\mathrm{tr}(\boldsymbol{T}^{\dagger
):=\gamma^{\mu}\cdot\boldsymbol{T}^{\dagger}(\gamma_{\mu})=\boldsymbol{T
^{\dagger}(\gamma^{\mu})\cdot\gamma_{\mu}.\label{35}\\
\mathrm{bif}(\boldsymbol{T})  &  =-\mathrm{bif}(\boldsymbol{T}^{\dagger
})=-\boldsymbol{T}^{\dagger}(\gamma_{\mu})\wedge\gamma^{\mu}=\gamma^{\mu
}\wedge\boldsymbol{T}^{\dagger}(\gamma_{\mu}). \label{35a
\end{align}
Now, the $\langle\rangle_{0}$ part of Eq.(\ref{7}) is taking into account
that\footnote{Note that $\phi_{L}\cdot\phi_{R}=\phi_{L}\cdot\phi_{L}=\phi
_{R}\cdot\phi_{R}.$}
\begin{equation}
\gamma^{\mu}\cdot\langle\partial_{\mu}\phi_{L}\gamma_{012}\phi_{R}\rangle
_{1}=eA\cdot J+m\phi_{L}\cdot\phi_{R}. \label{36
\end{equation}
Then
\begin{equation}
tr(\boldsymbol{T})=m\phi_{L}\cdot\phi_{R} \label{37
\end{equation}

Now, taking the $\langle\rangle_{0}$ part of Eq.(\ref{7}) we get
\begin{equation}
\frac{1}{2}\boldsymbol{\partial\lrcorner}(\gamma_{5}s)+\gamma^{\mu
\wedge\langle\partial_{\mu}\phi_{L}\gamma_{012}\phi_{R}\rangle_{1}=eA\wedge J
\label{38
\end{equation}
and then recalling also that $\boldsymbol{\partial\lrcorner}(\gamma
_{5}s)=-\gamma_{5}\boldsymbol{\partial\wedge}s
\begin{equation}
\mathrm{bif}(\boldsymbol{T})=\frac{1}{2}\gamma_{5}\boldsymbol{\partial\wedge
}s. \label{39
\end{equation}

Also, since
\begin{equation}
\boldsymbol{T}^{\dagger}(n)-\boldsymbol{T}(n)=n\lrcorner\mathrm{bif
(\boldsymbol{T}) \label{40
\end{equation}
we have
\begin{gather}
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial T}^{\dagger
(n)-\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial T
(n)=\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial}(n\lrcorner
\mathrm{bif}(\boldsymbol{T}))\nonumber\\
=\gamma^{\mu}\cdot\boldsymbol{\partial}_{n}[\partial_{\mu}n\lrcorner
\mathrm{bif}(\boldsymbol{T})+n\lrcorner\partial_{\mu}\mathrm{bif
(\boldsymbol{T})]\nonumber\\
=\boldsymbol{\partial}\lrcorner\mathrm{bif}(\boldsymbol{T
)=-\boldsymbol{\partial}\lrcorner(\boldsymbol{\partial\lrcorner}(\gamma
_{5}s)=-\boldsymbol{\delta}\lrcorner(\boldsymbol{\delta\lrcorner}(\gamma
_{5}s)=0 \label{41a
\end{gather}
which means that
\begin{equation}
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial T}^{\dagger
(n)=\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial T}(n). \label{42
\end{equation}

\subsection{The Source of Spin Extensor of the Dirac-Hestenes
Field\label{sourcesp}}

Taking advantage that Minkowski spacetime is parallelizable we introduce the
$1$-form
\begin{equation}
\boldsymbol{x}:=x^{\mu}\gamma_{\mu} \label{43
\end{equation}
which will be called the position $1$-form of a point of $x\in M$ relative to
the point $x_{0}\in M$ which is the one mapped to the origin of the
coordinates in $\mathbb{R}^{4}$. If we make the exterior product of both
members of Eq.(\ref{29}) by $\boldsymbol{x}$ we ge
\begin{equation}
\lbrack\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial T}(n)]\wedge
\boldsymbol{x}=e(F\llcorner J)\wedge\boldsymbol{x} \label{44
\end{equation}
using the identit
\begin{equation}
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial\lbrack\boldsymbol{T
}(n)\boldsymbol{\wedge\boldsymbol{x}]}=[\boldsymbol{\partial}_{n
\cdot\boldsymbol{\partial T}(n)]\wedge\boldsymbol{x}+\mathrm{bif
(\boldsymbol{T}) \label{45
\end{equation}
in Eq.(\ref{44}) we ge
\begin{equation}
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial\lbrack\boldsymbol{T
}(n)\boldsymbol{\wedge\boldsymbol{x}]}-\mathrm{bif}(\boldsymbol{T
)=e(F\llcorner J)\wedge\boldsymbol{x}. \label{46
\end{equation}

Now, we have that
\begin{gather*}
\mathrm{bif}(\boldsymbol{T})=\frac{1}{2}\gamma_{5}\boldsymbol{\partial\wedge
}s=-\frac{1}{2}\gamma_{5}\boldsymbol{\partial}_{\mu}(s\wedge\gamma^{\mu})\\
=-\frac{1}{2}\gamma^{\mu}\cdot\boldsymbol{\partial}_{n}\gamma_{5
[\boldsymbol{\partial}_{\mu}s\wedge n+s\wedge\boldsymbol{\partial}_{\mu
}\boldsymbol{x}]\\
-\gamma^{\mu}\cdot\boldsymbol{\partial}_{n}\boldsymbol{\partial}_{\mu}\frac
{1}{2}\gamma_{5}(s\wedge n)=-\boldsymbol{\partial}_{n}\cdot
\boldsymbol{\partial}\gamma_{5}(s\wedge n)
\end{gather*}
and introducing the $(1,2)$-extensor field
\begin{gather}
\boldsymbol{S}:\se
{\textstyle\bigwedge\nolimits^{1}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta})\rightarrow\se
{\textstyle\bigwedge\nolimits^{2}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta}),\nonumber\\
\boldsymbol{S}(n):=\frac{1}{2}\gamma_{5}(s\wedge n) \label{47
\end{gather}
called the \emph{spin extensor field} of the Dirac field we have that
\begin{equation}
\mathrm{bif}(\boldsymbol{T})=-\boldsymbol{\partial}_{n}\cdot
\boldsymbol{\partial S}(n) \label{48
\end{equation}
If we contract Eq.(\ref{48}) on the left taking account of Eq.(\ref{40}) we
get the fundamental resul
\begin{equation}
\boldsymbol{T}(n)-\boldsymbol{T}^{\dagger}(n)=n\lrcorner(\boldsymbol{\partial
}_{n}\cdot\boldsymbol{\partial S}(n)) \label{49
\end{equation}
which says that the source of the spin extensor is the antisymmetric part of
the energy-momentum extensor. From Eq.(\ref{49}) we can immediately get that
\begin{align}
T^{\mu\nu}-T^{\nu\mu}  &  =-\gamma^{\nu}\lrcorner(\gamma^{\mu}\lrcorner
(\boldsymbol{\partial}_{\kappa}\boldsymbol{S}(\gamma^{\kappa})))\nonumber\\
&  =-(\gamma^{\nu}\wedge\gamma^{\mu})\lrcorner\boldsymbol{\partial}_{\kappa
}\boldsymbol{S}(\gamma^{\kappa}). \label{50
\end{align}

Finally calling
\begin{equation}
\boldsymbol{J}(n):=\boldsymbol{T}(n)\wedge\boldsymbol{x}+\boldsymbol{S}(n)
\label{51
\end{equation}
t we get using Eq.(\ref{48}) on the left side of Eq.(\ref{46})
\begin{equation}
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial J}(n)=e(F\llcorner
J)\wedge\boldsymbol{x} \label{52
\end{equation}
Recalling that $(F\llcorner J)\wedge\boldsymbol{x}$ is the torque produced by
the Lorentz force $e(F\llcorner J)$ we see that Eq.(\ref{52}) says explicitly
that in the presence of an external electromagnetic field the total angular
momentum of the Dirac field is not conserved.

\subsection{Origin of the Bohm-Aharonov Effect

\begin{equation}
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial T}^{\dagger}(n)=eF\lrcorner
J
\end{equation}

In our opinion Eq.(\ref{29}) and Eq.(\ref{52}) encode the origin of the
Bohm-Aharonov effect. Indeed, recalling Eq.(\ref{28}) and Eq.(\ref{51}) we
hav
\begin{align*}
\boldsymbol{T}(n)  &  =\boldsymbol{T}_{D}(n)-en\cdot AJ,\\
\boldsymbol{J}(n)  &  :=\boldsymbol{T}_{D}(n)\wedge\boldsymbol{x
+\boldsymbol{S}(n)-en\cdot AJ\wedge\boldsymbol{x}=\boldsymbol{J
_{D}(n)-en\cdot AJ\wedge\boldsymbol{x
\end{align*}
So, it follows that even in spacetime regions with topology permitting that
$F=0$ but $A\neq0$ we must have (with $A=A^{\mu}\gamma_{\mu}$) from Eqs.
(\ref{29}) and (\ref{52}
\begin{align}
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial T}_{D}(n)  &
=\partial_{\mu}\boldsymbol{T}_{D}(\gamma^{\mu})=e\boldsymbol{\partial
_{n}\cdot\boldsymbol{\partial(}n\cdot AJ)=\partial_{\mu}(A^{\mu}J)\label{53}\\
\boldsymbol{\partial}_{n}\cdot\boldsymbol{\partial J}_{D}(n)  &
=\partial_{\mu}\boldsymbol{J}_{D}(\gamma^{\mu})=\boldsymbol{\partial}_{n
\cdot\boldsymbol{\partial}[n\cdot AJ\wedge\boldsymbol{x}]=\partial_{\mu
}(A^{\mu}J\wedge\boldsymbol{x}) \label{54
\end{align}
which says that in regions where $F=0$ but $A\neq0$ the energy-momentum
$\boldsymbol{T}_{D}(n)$ and the total angular-momentum extensor
$\boldsymbol{J}_{D}(n)$ of the Dirac field are \emph{not }conserved. This
certainly means that a particle described by a Dirac field entering a region
with topology permitting that $F=0$ but $A\neq0$ will follows paths distinct
from the ones where it enter a region where $F=0$ and $A=0$. This is exactly
what is predicted in the Bohm-Aharonov effect and the experimental study of
the possible trajectories (as done, e.g., in) in the de Broglie-Bohm
interpretation of the Dirac equation seems a good test for such interpretation
of quantum mechanics.

\section{The Correct Relativistic Quantum Potential}

In this section we analyze in details papers \cite{hc1,hc2} showing that it
contains erroneous results and thus an erroneous identification of the quantum
potential. Moreover, we recall form our recent paper \cite{rw2016a} where we
derive the correct generalized Hamilton-Jacobi equation which follows from the
DHE satisfied by a DHSF and identifies the correct relativistic quantum potential.

So, to start our analysis, recall that from Eq.(\ref{30}) we can write for the
energy-momentum $1$-form fields $\boldsymbol{T}_{D}^{\dagger^{\mu}}$ that
\begin{equation}
\boldsymbol{T}_{D}^{\dagger^{\mu}}=\langle\partial^{\mu}\phi_{L}\gamma
_{012}\phi_{R}\rangle_{1}=\frac{1}{2}\left(  \partial^{\mu}\phi_{L
\gamma_{012}\phi_{R}-\phi_{L}\gamma_{012}\partial^{\mu}\phi_{R}\right)
\label{55
\end{equation}

In \cite{hc1,hc2} authors define the objects
\begin{equation}
\rho\mathbf{P}^{\mu}=\frac{1}{2}\left(  \partial^{\mu}\phi_{L}\gamma_{012
\phi_{R}-\phi_{L}\gamma_{012}\partial^{\mu}\phi_{R}\right)  \label{56
\end{equation
\begin{gather}
\rho\mathbf{W}^{\mu}=-\frac{1}{2}\partial^{\mu}(\phi_{L}\gamma_{012}\phi
_{R})\nonumber\\
=-\frac{1}{2}[\partial^{\mu}\phi_{L}\gamma_{012}\phi_{R}+\phi_{L}\gamma
_{012}\partial^{\mu}\phi_{R}]=-\langle\partial^{\mu}\phi_{L}\gamma_{012
\phi_{R}\rangle_{3} \label{57
\end{gather}
which taking into account Eqs.(\ref{3}) and (\ref{9}) permit us to writ
\begin{align}
\rho\mathbf{P}^{\mu}  &  =\boldsymbol{T}_{D}^{\dagger^{\mu}}=\langle
\partial^{\mu}\phi_{L}\gamma_{012}\phi_{R}\rangle_{1}\in\se
{\textstyle\bigwedge\nolimits^{1}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta})\label{58}\\
\rho\mathbf{W}^{\mu}  &  =-\langle\partial^{\mu}\phi_{L}\gamma_{012}\phi
_{R}\rangle_{3}\in\se
{\textstyle\bigwedge\nolimits^{3}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta}) \label{59
\end{align}
Authors of \cite{hc1,hc2} also introduce the object\footnote{Take notice that
the object $\mathbf{J}$ is not the same object we call $J$ (the probability
current) given by Eq.(\ref{8}) and is also different from the total angular
momentum extensor which we denoted by $\boldsymbol{J}(n)$.}
\begin{equation}
\rho\mathbf{J}:=\phi_{L}\gamma_{012}\phi_{R}\in\se
{\textstyle\bigwedge\nolimits^{1}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta}) \label{60
\end{equation}

Now, recall that for a Dirac particle moving in a region where $A=0$,
Eq.(\ref{15}) become

\begin{equation}
\boldsymbol{\partial}^{2}\phi_{L}+m^{2}\phi_{L}=0 \label{61
\end{equation}
and of course we have also that
\begin{equation}
\boldsymbol{\partial}^{2}\phi_{R}+m^{2}\phi_{R}=0. \label{62
\end{equation}
Multiplying Eq.(\ref{61}) on the right by $\phi_{R}$ and Eq.(\ref{62}) on the
right by $\phi_{L}$ and taking first the sum of these equations and second
their difference we get $\partial_{\mu}\partial^{\mu}
\begin{equation}
\partial_{\mu}(\partial^{\mu}\phi_{L})\phi_{R}+\phi_{L}(\partial_{\mu
\partial^{\mu}\phi_{R})+2m^{2}\phi_{L}\phi_{R}=0 \label{63
\end{equation}
and
\begin{equation}
\phi_{L}(\partial_{\mu}\partial^{\mu}\phi_{R})-\partial_{\mu}(\partial^{\mu
}\phi_{L})\phi_{R}=0 \label{64
\end{equation}
Now, suppose that $\phi_{L}$ is such that
\begin{equation}
\phi_{L}\tilde{\phi}_{L}=\phi_{L}\phi_{R}\neq0. \label{65
\end{equation}
Then $\phi_{L}$ is invertible and can be written
\begin{equation}
\phi_{L}=R\text{ }e^{\frac{1}{2}\gamma_{5}\beta}U \label{66
\end{equation}
where $R$,$\beta$ are scalar functions\footnote{The function $\beta$ is called
the Takabayshi angle.} (0-form fields) and for each $x\in M$, $U\in
\mathrm{Spin}_{1,3}^{0}(\simeq\mathrm{Sl}(2,\mathbb{C}))\subset\mathbb{R
_{1.3}^{0}$ and so $U\tilde{U}=\tilde{U}U=1.$ Putting $\rho=R^{2}$ from
Eqs.(\ref{56}) and (\ref{57}) we immediately get
\begin{align}
-\partial^{\mu}\phi_{L}  &  =[\mathbf{P}^{\mu}-\mathbf{W}^{\mu}]\phi
_{L}e^{-\gamma_{5}\beta}\gamma_{012},\label{67}\\
\partial^{\mu}\phi_{R}  &  =\gamma_{012}\phi_{R}e^{-\gamma_{5}\beta
}[\mathbf{P}^{\mu}+\mathbf{W}^{\mu}]. \label{68
\end{align}

\begin{remark}
Now, comes an important and crucial observation. Authors of
\emph{\cite{hc1,hc2}} write \emph{Eqs.(\ref{67}}) and \emph{(\ref{68})}
\ without the term $e^{-\gamma_{5}\beta}$. This means that they took the
Takabayashi angle as null. In \cite{rw2016a} we called \ invertible spinor
fields for which $\beta=0$ or $\pi$ classical spinor fields. The reason for
that name was that in \cite{rw2016a} we prove that the classical
Hamilton-Jacobi equation for a an electrical particle moving in an external
field $A$ is equivalent to a DHE satisfied by a classical Dirac-Hestenes
spinor field and that a DHE satisfied by a classical Dirac-Hestenes spinor
field is equivalent to the classical Hamilton-Jacobi equation. This classical
Dirac-Hestenes spinor field has the form
\begin{align}
\phi_{L}  &  =R\mathfrak{R}(\Pi)e^{S\gamma^{21}},\nonumber\\
\mathfrak{R}(\Pi)  &  =\frac{m+(\Pi+eA)\gamma^{0}}{\left[  2\left(  m+\Pi
_{0}+A_{0}\right)  \right]  ^{1/2}}, \label{69
\end{align}
wit
\begin{equation}
\Pi:-\partial S=mV+eA \label{70
\end{equation}
being the canonical momentum and
\begin{equation}
V=\phi_{L}\gamma^{0}\phi_{L}^{-1} \label{71
\end{equation}
being the \emph{(}$1$-form\emph{)} velocity field such that for each possible
world line of the classical particle \emph{(}parametrized with the proper
time\emph{)} $\sigma:\mathbb{R\rightarrow}M$ we have
\begin{equation}
\left.  \mathtt{\eta}(V,~)\right\vert _{\sigma}=\sigma_{\ast}=v \label{76
\end{equation}
where $v$ is the velocity of the particle.

To end this remark we present\emph{ \cite{rw2016a}} the correct generalized
Hamilton-Jacobi equation \emph{(GHJE)} that follows almost trivially in our
formalism for the \emph{DHE} satisfied by a general free \emph{DHSF} that we
write a
\begin{equation}
\boldsymbol{\psi}=\boldsymbol{\rho}^{1/2}\mathcal{R}(\Pi)e^{\frac{\beta
\gamma^{5}}{2}}e^{S\gamma^{21}}=\boldsymbol{\psi}_{0}e^{\frac{\beta\gamma^{5
}{2}}e^{S\gamma^{21}}=e^{\frac{\beta\gamma^{5}}{2}}\boldsymbol{\psi
_{0}e^{S\gamma^{21}}.
\end{equation}
in interaction with an external electromagnetic field. It is, with
\emph{(}$\Pi=-\boldsymbol{\partial}S$ and $\boldsymbol{\psi}\gamma
^{0}\boldsymbol{\psi}^{-1}=e^{\beta\gamma^{5}}V$
\begin{equation}
-\boldsymbol{\partial}S=m\cos\beta V+eA+\langle m\sin\beta\gamma
^{5}V+(\boldsymbol{\partial}\ln\boldsymbol{\psi}_{0})\boldsymbol{\psi
\gamma^{21}\boldsymbol{\psi}^{-1}+\frac{1}{2}\gamma^{5}\boldsymbol{\partial
}(\ln\beta)\boldsymbol{\psi\rangle}_{1} \label{76aa
\end{equation}
where the following constraint must hold
\begin{equation}
\langle e\sin\beta\gamma^{5}V+(\boldsymbol{\partial}\ln\boldsymbol{\psi
_{0})\boldsymbol{\psi}\gamma^{21}\boldsymbol{\psi}^{-1}+\frac{1}{2}\gamma
^{5}\boldsymbol{\partial}(\ln\beta)\boldsymbol{\psi\rangle}_{3}=0 \label{76ac
\end{equation}

Thus the true "quantum potential" is
\begin{equation}
Q=\langle m\sin\beta\gamma^{5}V+(\boldsymbol{\partial}\ln\boldsymbol{\psi
_{0})\boldsymbol{\psi}\gamma^{21}\boldsymbol{\psi}^{-1}+\frac{1}{2}\gamma
^{5}\boldsymbol{\partial}(\ln\beta)\boldsymbol{\psi\rangle}_{1}\label{76ad
\end{equation}
which differs considerably form the usual Bohm quantum potential. Moreover and
contrary to the usual presentations of the de Broglie-Bohm theory the mass
parameter of the\ particle in the \emph{GHJE} \emph{(Eq.(\ref{76aa})) }is not
a constant, instead it i
\begin{equation}
m^{\prime}=m\cos\beta.\label{76ae
\end{equation}

Some analogous results using classical like equations of motion isntead of the
Hamilton Jacobi like equation as above has been obtained in a series of
remarkable papers by Hestenes \cite{hestenes1,hestenes2,hestenes3}.
\end{remark}

Now, we returning to the analysis of papers \cite{hc1,hc2} where as shown
above used $\beta=0$. Under these conditions if we substitute Eqs.(\ref{67})
and (\ref{68}) in Eq.(\ref{63}) we ge

\begin{align}
&  \rho(\mathbf{P}^{\mu}\mathbf{P}_{\mu}+\mathbf{W}^{\mu}\mathbf{W}_{\mu
})\nonumber\\
&  +\rho(\partial_{\mu}\mathbf{P}^{\mu}\mathbf{J}-\mathbf{J}\partial_{\mu
}\mathbf{P}^{\mu})\nonumber\\
&  -\rho(\partial_{\mu}\mathbf{W}^{\mu}\mathbf{J}+\mathbf{J}\partial_{\mu
}\mathbf{W}^{\mu})-m^{2}\rho=0 \label{76a
\end{align}

Now, since $\langle\mathbf{W}^{\mu}\mathbf{W}_{\mu}\rangle_{2}=-\langle
\mathbf{W}^{\mu}\mathbf{W}_{\mu}\rangle_{2}=0$ we have tha
\begin{align}
&  (\mathbf{P}^{\mu}\mathbf{P}_{\mu}+\mathbf{W}^{\mu}\mathbf{W}_{\mu
})\nonumber\\
&  =\mathbf{P}^{\mu}\lrcorner\mathbf{P}_{\mu}+\langle\mathbf{W}^{\mu
}\mathbf{W}_{\mu}\rangle_{0}+\langle\mathbf{W}^{\mu}\mathbf{W}_{\mu
\rangle_{2}\nonumber\\
&  =\mathbf{P}^{\mu}\lrcorner\mathbf{P}_{\mu}+\mathbf{W}^{\mu}\lrcorner
\mathbf{W}_{\mu} \label{76c
\end{align
\begin{align}
&  (\partial_{\mu}\mathbf{P}^{\mu}\mathbf{J}-\mathbf{J}\partial_{\mu
}\mathbf{P}^{\mu})\nonumber\\
&  =2\partial_{\mu}\mathbf{P}^{\mu}\wedge\mathbf{J.} \label{76b
\end{align}
Since\footnote{Note that for any $A,B\in\se
{\textstyle\bigwedge\nolimits^{3}}
T^{\ast}M\hookrightarrow\sec\mathcal{C\ell}(M,\mathtt{\eta})$ always $\langle
AB\rangle_{4}=0$.} $\langle\partial_{\mu}\mathbf{W}^{\mu}\mathbf{J}\rangle
_{4}=0$ and $\langle\partial_{\mu}\mathbf{W}^{\mu}\mathbf{J}\rangle_{2}=-$
$\langle\mathbf{\tilde{J}}\partial_{\mu}\mathbf{\tilde{W}}^{\mu}\rangle
_{2}=-\langle\mathbf{J}\partial_{\mu}\mathbf{W}^{\mu}\rangle_{2}$ it is
\begin{equation}
-(\partial_{\mu}\mathbf{W}^{\mu}\mathbf{J}+\mathbf{J}\partial_{\mu
\mathbf{W}^{\mu})=-2\partial_{\mu}\mathbf{W}^{\mu}\lrcorner\mathbf{J.}
\label{76C
\end{equation}

Then, Eq.(\ref{76a}) become

\begin{equation}
\mathbf{P}^{\mu}\lrcorner\mathbf{P}_{\mu}+\mathbf{W}^{\mu}\lrcorner
\mathbf{W}_{\mu}+2\partial_{\mu}\mathbf{P}^{\mu}\wedge\mathbf{J
-2\langle\partial_{\mu}\mathbf{W}^{\mu}\mathbf{J}\rangle_{0}-m^{2}=0
\label{76HC
\end{equation}
which implies that

\begin{gather}
\mathbf{P}^{\mu}\lrcorner\mathbf{P}_{\mu}+\mathbf{W}^{\mu}\lrcorner
\mathbf{W}_{\mu}-2\langle\partial_{\mu}\mathbf{W}^{\mu}\mathbf{J}\rangle
_{0}-m^{2}=0,\label{76e}\\
2\partial_{\mu}\mathbf{P}^{\mu}\wedge\mathbf{J=0.} \label{76f
\end{gather}

Now (with $\beta=0$), substituting Eqs.(\ref{67}) and (\ref{68}) in
Eq.(\ref{64}) we ge

\begin{gather}
\underset{X}{\underbrace{2\rho\mathbf{J}\partial^{\mu}\mathbf{P}_{\mu
+2\rho\mathbf{J}\partial^{\mu}\mathbf{W}_{\mu}+2\rho\partial^{\mu
\mathbf{P}_{\mu}\mathbf{J}-2\rho\partial^{\mu}\mathbf{W}_{\mu}\mathbf{J}
}\nonumber\\
+\text{ }\underset{Y}{\underbrace{\phi_{L}\gamma_{012}\boldsymbol{\partial
}^{\mu}\phi_{R}\mathbf{P}_{\mu}+\mathbf{P}_{\mu}\boldsymbol{\partial}^{\mu
}\phi_{L}\gamma_{012}\phi_{R}}}\nonumber\\
+\text{ }\underset{Z}{\underbrace{\phi_{L}\gamma_{012}\boldsymbol{\partial
}^{\mu}\phi_{R}\mathbf{W}_{\mu}+\mathbf{W}_{\mu}\boldsymbol{\partial}^{\mu
}\phi_{L}\gamma_{012}\phi_{R}}
\begin{array}
[c]{c
\\
=0\\
\end{array}
\label{77
\end{gather}

Calling the contents of the three lines of Eq.(\ref{77}) respectively $X,Y,Z$
we have
\begin{align}
X  &  =4\rho\partial^{\mu}\mathbf{P}_{\mu}\lrcorner\mathbf{J}\boldsymbol{+
2\rho\langle\mathbf{J}\partial^{\mu}\mathbf{W}_{\mu}\rangle_{0}+2\rho
\langle\mathbf{J}\partial^{\mu}\mathbf{W}_{\mu}\rangle_{2}-2\rho
\langle\partial^{\mu}\mathbf{W}_{\mu}\mathbf{J}\rangle_{0}-2\rho
\langle\partial^{\mu}\mathbf{W}_{\mu}\mathbf{J}\rangle_{2}\nonumber\\
&  4\rho\partial^{\mu}\mathbf{P}_{\mu}\lrcorner\mathbf{J}+4\rho\langle
\mathbf{J}\partial^{\mu}\mathbf{W}_{\mu}\rangle_{2}, \label{78
\end{align
\begin{align}
Y  &  =-\rho(\mathbf{P}_{\mu}\mathbf{W}^{\mu}+\mathbf{W}^{\mu}\mathbf{P}_{\mu
})=\nonumber\\
&  =-\rho\lbrack\langle\mathbf{P}_{\mu}\mathbf{W}^{\mu}\rangle_{2
+\langle\mathbf{P}_{\mu}\mathbf{W}^{\mu}\rangle_{4}+\langle\mathbf{W}^{\mu
}\mathbf{P}_{\mu}\rangle_{2}+\langle\mathbf{P}_{\mu}\mathbf{W}^{\mu
\rangle_{4}]\nonumber\\
&  =-2\rho\langle\mathbf{P}_{\mu}\mathbf{W}^{\mu}\rangle_{2}=-2\rho
\mathbf{P}_{\mu}\lrcorner\mathbf{W}^{\mu}, \label{79
\end{align
\begin{equation}
Z=-\rho(\mathbf{P}_{\mu}\mathbf{W}^{\mu}+\mathbf{W}^{\mu}\mathbf{P}_{\mu});
\label{80
\end{equation}
So, Eq.(\ref{77}) become

\begin{equation}
\partial^{\mu}\mathbf{P}_{\mu}\lrcorner\mathbf{J}+\langle\mathbf{J
\partial^{\mu}\mathbf{W}_{\mu}\rangle_{2}-\mathbf{P}_{\mu}\lrcorner
\mathbf{W}^{\mu}=0. \label{84
\end{equation}

\begin{remark}
Authors of \cite{hc1,hc2} did not obtain \emph{Eqs.(\ref{76e}), (\ref{76f})}
and \emph{(\ref{84})} and moreover they interpreted the scalar part in
Eq.(\ref{76HC}) as being the GHJE in Bohm formalism. If this was the case we
would identify $(\mathbf{W}^{\mu}\lrcorner\mathbf{W}_{\mu}-2\langle
\partial_{\mu}\mathbf{W}^{\mu}\mathbf{J}\rangle_{0})$ as the quantum potential.

However we claim that such an identification is misleading in view of the
results presented in \textit{\cite{rw2016a}} and also from the fact that
authors of \emph{\cite{hc1,hc2}} wrongly identified $2\rho\mathbf{P}^{\mu}$
with the components $T_{D}^{\mu0}$ of the energy-momentum of the Dirac field,
which is a nonsequitur since the objects $2\rho\mathbf{P}^{\mu}$ are $1$-forms
and objects $T_{D}^{\mu0}$ are scalars. Moreover, for Dirac theory\ as
\emph{Eq.(76ad) }shows the quantum potential is a $1$-form field, not a scalar
function.$.$
\end{remark}

\begin{remark}
As a final remark, we emphasize that \emph{Eq.(\ref{84})} does not describe
the development of the spin. The equation of motion of the spin is the one
given by \emph{Eq.(\ref{38})}.
\end{remark}

\section{Conclusions}

Using the Clifford and spin-Clifford bundle formalisms and some few results of
the theory of extensor calculus we derived the conservation laws for the
probability current, energy-momentum and total angular momentum extensors
resulting from the structure of DHE satisfied by a Dirac-Hestenes spinor field
(DHSF) in interaction with the electromagnetic field. It was shown in a quite
simple way that the energy-momentum extensor\footnote{Related to theTetrode
tensor of the Dirac spinor field.} of the DHSF is not symmetric and that its
antisymmetric part is the \emph{source }of the spin extensor field of the free
DHSF. In particular it was shown that these conservation laws implies that in
spacetime regions with topology permitting the existence of an electromagnetic
field potential $A\neq0$ but with $F=0$ the energy-momentum and total angular
momentum of the sole DHSF are not conserved and this fact clearly is the
origin of the Bohm-Aharonov effect. And here it must be emphasize that since
this result can be directly derived \ for the DHE\ satisfied by a classical
DHSF equivalent to the classical relativistic HJE satisfied by a (spinning)
charged particle it is not of \ primely of quantum nature, more precisely, one
can predict that the motion of spinning charged particles in a region \ with
topology permitting $A\neq0$ but with $F=0$ is different from the motion of
spinning charged particles in a region $A=0$ but with $F=0$.

We also briefly recalled results obtained in \cite{rw2016a} where it was shown
that (a): that the classical\ relativistic Hamilton-Jacobi equation (HJE)
\ for a charged electrical particle in interaction with the electromagnetic
field is equivalent to a DHE satisfied by a special class of DHSF that we call
\emph{classical }DHSF which are characterized by having the Takabayashi angle
equal to $0$ or $\pi$ and moreover that the DHE satisfied by a classical DHSF
is equivalent to the HJE; (b) The identification of the correct relativistic
quantum potential resulting from the DHE in a de Broglie-Bohm approach
\cite{bh,debroglie} leading to a HJE like equation for the motion of
(spinning) charged particle. And equipped with these results and the ones of
Section 2 we analyzed results of \cite{hc1,hc2} were authors though that they
have disclosed the relativistic quantum potential for the Dirac particle. We
show that the results of those papers are equivocated \ by explicitly showing
with detailed calculations were authors get mislead.

In view of the recent interest on experiments to verify if the trajectories of
particles predicted by de Broglie-Bohm theory (see, e.g.,
\cite{englertetal,mahleretal,savantetal}) and pertinent criticisms, like,
e.g., in \cite{ck1,ck2,jonesetal} we think that our results are worth to be
appreciated. In particular, it clear for us that any prediction of
trajectories even in the nonrelativistic limit must be done using the non
relativistic approximation to the DHE, for as shown long ago in an important
paper by Guther and Hestenes \cite{gh1975} the Schr\"{o}dinger equation which
may be derived for the DHE in fact describes not a spinless particle, but a
particle in a spin auto state.

Concerning also the trajectories problem it is important to discover if
particles follows the integral lines of the velocity field as defined in
\cite{rw2016a} or the integral lines of the vector field $\mathtt{\eta
}(\boldsymbol{T}_{D}^{0},)=T_{D}^{0\mu}\frac{\partial}{\partial\mathrm{x
^{\mu}}$ (which are the ones appearing in the conservation laws of
energy-momentum and total angular momentum).

redpajama_set_name: RedPajamaArXiv


text:
Home National Tea Sellers Daughter Aanchal Gangwal Becomes Fighter Pilot
Tea Sellers Daughter Aanchal Gangwal Becomes Fighter Pilot
Aanchal Gangwal, a 26-year-old daughter of a small tea stall in Neemuch, Madhya Pradesh, has become a fighter aircraft pilot in the Air Force. Anchal honour at the initiation ceremony held in Hyderabad. Air Chief Marshal RKS Bhadauria dedicated Aanchal and other trainees to the country service. This achievement of the daughter brings happiness to the family members, including her father.
At Neemuch's bus stand, Anchal's father Suresh Gangwal runs a small tea shop. Aanchal was successful in the Air Force Common Admission Test in the year 2018. In June 2018, she left for Hyderabad for a training fighter pilot. The father flees the daughter's dreams despite running a tea shop. Apart from his father, mother Babita, brother Chandresh (electrical engineer in Indore) and sister Divyani (volleyball player) are in Anchal's family. The Gangwal family is originally from Tarapur-Ummedpura village in Javad development block in Neemuch district.
Inspired By The 2013 Event
Aanchal inspired to join the Air Force through a 2013 incident. Aanchal said that in 2013 there was a devastating flood in Uttarakhand. During this time, the Indian Air Force carried out the rescue operation well. Seeing this work on TV inspired him to join the Air Force. At that time, Anchal was studying in class 12.
Aanchal Gangwal Success Rate Success
April 2017: Selected as Sub-Inspector in the Police Department. After Dhar, Sagar went on training. Resigned from this post in August 2017.
August 2017: Anchal selected as Labor Inspector. She was posted as a labour inspector in Mandsaur for several months.
June 2018 to June 2020: Success in the Air Force Common Admission Test. She was the only woman from MP to be selected.
Training started at Hyderabad Air Force Academy from 30 June 2018. On 20 June 2020, the initiation parade took place after practice.
We Did Not Lose Courage: Suresh.
Aanchal Gangwal, daughter of Suresh Gangwal, who sells tea in Neemuch, Madhya Pradesh, who is a flying officer in the IAF, was awarded the President's plaque on Saturday. Suresh said that people of small category like us face problems, but we did not lose courage and did not let the children also suffer.
Father Given The Most Precious Gift On Father's Day
Suresh Gangwal said that on Saturday, daughter Anchal Gangwal had received a commission in the Indian Airforce. Aanchal's parents could not attend the passing out parade held at Dundigal AFA, but there was a wave of happiness in the family after watching the daughter's success on TV. Gangwal says that on Father's Day 2020, Beti Anchal has given the most significant gift by achieving success.
Aanchal Gangwal Father Sells Tea in Neemuch
Anchal's father Suresh Gangwal sells tea in Neemuch. She had to go to Hyderabad to see her daughter's success. But he has seen this entire event online from home. Suresh Gangwal has taught his three children by selling tea. Suresh's elder son is an engineer. The second daughter is Aanchal Flying Officer, while the youngest daughter is doing B Com. On the success of her daughter, she has said that she should never be afraid of troubles.
Aanchal Gangwal Has Left Two Gobs
During the Kedarnath tragedy, Anchal decided to join the force. At that time she was studying in 12th standard. Aanchal was hardworking from the beginning. First, he got the job of police sub-inspector in MP, he quit after a few days. Then Anchal was selected as the Labor Inspector. But his motive was to go into the force. Hence, she later left the job of Labor Inspector.
Did Not Even Drink Water In The Practice Period For Three Days
Anishal's physical trainer Kishan Pal told that I remember how hard his father taught that girl. That girl's most challenging time was when she told me that sir I have 24 days and I have to lose 9 kg. Aanchal Gangwal did not even drink water in the practice period for three days.
Aanchal Gangwal
Aanchal Gangwal Becomes Fighter Pilot
Aanchal Gangwal Fighter Pikot
Aanchal Gangwal News
Aanchal Gangwal Pilot
Nimach
Tea Sellers Daughter
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3 Tips to Save Money on your Halloween Costume!
1. Work with what you have!
Look around your house and see what you can put together with what you have! These two costumes were put together with things they already had! In the hunter and fox image, big sister is wearing baby brother's sweatshirt!
Get crafty! Check out Pinterest if you need ideas or tutorials, but there are so many ideas out there and they don't have to be pricey or difficult! This sweet mama made costumes for her kiddos when they wanted to be a marshmallow and an owl!
3. Check your consignment shop!
Consignment shops are full of costumes this time of year! This is a great way to snag a costume for your kiddo at a fraction of the cost! Better yet, consign last year's costume for a credit toward this year's!


text:
The Cost of Inclusion: Race, Class, Gender, and the Social Dynamics of College Life
Silver, Blake, Sociology - Graduate School of Arts and Sciences, University of Virginia
Roksa, Josipa, Department of Sociology, University of Virginia
Sociological theory highlights the role of culture in reproducing social inequality, especially in educational settings. Existing research has focused on illuminating the role of exclusive cultural resources in facilitating success in schools. While offering valuable insights into the capacity of culture to exclude, prior literature has offered comparatively limited insights into the role of culture in finding inclusion.
Drawing on the insights of interaction ritual theorists like Erving Goffman and Randall Collins, I examine students' pursuit of inclusion in college. More specifically, I conducted an ethnographic study at a large, public university, observing three groups of college students over the course of an academic year and interviewing 60 first-year students during the spring semester. Through this approach, I sought to understand (1) how students pursue social inclusion within peer groups, and (2) how students make meaning of their experiences in these groups.
The results indicate that race, class, and gender intersect in shaping students' experiences with the social landscape of college in unique ways. Social class impacts students' approaches to locating social groups with the potential to offer social connections. While more socioeconomically advantaged students take an intentional, strategic approach, their less advantaged peers often engage in a more haphazard process of finding groups. However, beyond the point of locating groups, the impact of social class on student experiences is less evident as the influence of race and gender become pronounced when students seek to manage their social involvement and interact with their peers.
Within groups, students take on simplistic, culturally recognizable styles of self-presentation that correspond with distinct social roles. Each of these roles in turn require behaviors that link to feelings of value and belonging for their occupants. Notably, the styles of self-presentation characteristic of each role also carry raced and gendered associations that make some of the most central and highly valued roles inaccessible to female and racial/ethnic minority students. Conversely, White male students are allowed – and even encouraged – to take on styles of self-presentation that position them as central members of the group and amplify their sense of belonging. The roles students adopt allow them to become part of groups where they can feel connection, while simultaneously stratifying group membership. By bringing together two elements of culture – namely interactional styles as well as raced and gendered meanings – these findings offer new ways of understanding the complex role of culture in facilitating inclusion while maintaining inequality.
Inequality, Culture, Higher Education, Inclusion, Race, Social Class, Gender, Interaction
All rights reserved (no additional license for public reuse)
https://doi.org/10.18130/V3FX73X4K
This item is restricted to UVA until November 22, 2022.


text:
Study Shows Middle-Class Wages Have Stagnated Over Time
University of Minnesota, Twin Cities
It's getting harder for most American workers to get by.
Middle- and working-class workers' earnings in the US have been stagnating or sinking in recent decades, according to a study conducted by a group of researchers that included the University of Minnesota's Fatih Guvenen, Ph.D., Curtis L. Carlson professor of economics in the College of Liberal Arts. The team's research, recently covered in a Washington Post article, explores how the lifetime income for men and women in the US has changed over six decades, from 1957 to 2013.
The study, which used records from the US Social Security Administration to track the individual income of millions of people over the course of their lives, was published as a working paper by the National Bureau of Economic Research in April. Guvenen collaborated with researchers from the University of Chicago, Princeton University and the Social Security Administration to conduct the research.
Despite the growth of the nation's overall economy, the study notes that workers who entered the workforce in 1983 made about $283,000 less during their lifetimes—$243,000 less when factoring in employment benefits separate from pay—than workers who entered the workforce in 1967, when using the Consumer Price Index to account for inflation. Meanwhile, the wealthiest workers have benefited from more and more economic gains, increasing the gap between the rich and everyone else.
The study set out in part to shed more light on an economic trend that has persisted since the 1970s: stagnating average incomes. While many economic studies have tried to understand this trend by looking at income data from any given point in time, this study considered the total earnings an individual brings in during their lifetime.
Changes over the decades have decreased the earnings gap between genders, the study found, with men's wages lowering and women's generally rising, although women are still making less than men over their lifetimes. Men entering the workforce in 1983, for example, earned 10–19 percent less over their lifetime (depending on the measure of inflation used) than those who entered the workforce in 1967. The same timeline saw women's income grow 22–33 percent, though the rise in women's earnings has stalled more recently. Overall, growth in women's wages did not offset the decrease men's income across the population.
By comparing early-career earnings to lifetime income, the study found that workers' average income at age of 25 (toward the beginning of their careers) can effectively forecast their lifetime earnings. The researchers believe that, moving forward, the key to understanding exactly why wages are stagnating or decreasing may lie in examining the beginning of their careers.
"In order to understand why the US income distribution has changed dramatically over the past 50 years," the authors wrote, "we need to better understand the experiences of newer cohorts during their youth (and possibly earlier), and how those experiences differ from older cohorts."
Moving forward, the study could set the stage for additional research that may shed light on the specific causes of the middle class's decline—and possibly lead to recommendations that economists and policymakers can use to help prevent it.
By Kevin Coss
Study Shows Middle-Class Wages Have Stagnated Over Time was originally published on the University of Minnesota website
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Curly scarf for a warm wrap around your neck this winter. If only takes one skein of the glorious NORO Kochoran.
Kit includes the pattern and one ball of Kochoran. Just select the colour yarn you would like.
This pattern comes in 2 sizes: adult or child.
The pattern will be emailed to you are purchase.