# Tagged Questions

Quantum-ElectroDynamics (QED) is the quantum field theory believed to describe the electromagnetic interaction (and with some extension the weak nuclear force).

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### Why did Feynman's thesis almost work?

A bit of background helps frame this question. The question itself is in the last sentence. For his PhD thesis, Richard Feynman and his thesis adviser John Archibald Wheeler devised an astonishingly ...
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### How are classical optics phenomena explained in QED (Snell's law)?

How is the following classical optics phenomenon explained in quantum electrodynamics? Reflection and Refraction Are they simply due to photons being absorbed and re-emitted? How do we get to ...
1answer
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### Spontaneous breaking of Lorentz invariance in gauge theories

I was browsing through the hep-th arXiv and came across this article: Spontaneous Lorentz Violation in Gauge Theories. A. P. Balachandran, S. Vaidya. arXiv:1302.3406 [hep-th]. (Submitted on 14 ...
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369 views

### how is shown that photon speed is constant using QED?

In Feynman's simple QED book he talks about the probability amplitude P(A to B) ,where A and B are events in spacetime, and he says that it depends of the spacetime interval but he didn't put the ...
3answers
627 views

### Simple (but wrong) argument for the generality of positive beta-functions

In the introduction (page 5) of Supersymmetry and String Theory: Beyond the Standard Model by Michael Dine (Amazon, Google), he says (Traditionally it was known that) the interactions of ...
2answers
263 views

### What tree-level Feynman diagrams are added to QED if magnetic monopoles exist?

Are the added diagrams the same as for the $e-\gamma$ interaction, but with "$e$" replaced by "monopole"? If so, is the force between two magnetic monopoles described by the same virtual ...
4answers
725 views

### QM and Renormalization (layman)

I was reading Michio Kaku's Beyond Einstein. In it, I think, he explains that when physicsts treat a particle as a geometric point they end up with infinity when calculating the strength of the ...
3answers
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### Can the path of a charged particle under the influence of a magnetic field be considered piecewise linear?

Ordinarily we consider the path of a charged particle under the influence of a magnetic field to be curved. However, in order for the trajectory of the particle to change, it must emit a photon. ...
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### how does dynamic casimir effect generate correlated photons

There is a recent paper on arxiv receiving lot of acclaim http://arxiv.org/abs/1105.4714 The authors experimentally show that moving a mirror of a cavity at high speeds produces light from high ...
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### Using photons to explain electrostatic force

I am trying to understand the idea of a force carrier with the following example. Let's say there are two charges $A$ and $B$ that are a fixed distance from each other. What is causing the force on ...
4answers
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### The Schwinger model

The Schwinger model is the 2d QED with massless fermions. An important result about it (which I would like to understand) is that this is a gauge invariant theory which contains a free massive vector ...
2answers
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### Virtual photon description of B and E fields

I continue to find it amazing that something as “bulky” and macroscopic as a static magnetic or electric field is actually a manifestation of virtual photons. So putting on your QFT spectacles, look ...
3answers
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### Why muonium is unstable?

This question is closely related to my previous question Bound states in QED. Muonium is a system of electron and anti-muon. This article in wikipedia claims that muonium is unstable. QUESTION: Why ...
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319 views

### Quantizing EM field

Why when we quantize EM field, whe quantize the vector potential $A^\mu$ obtaining vectorial particles (photons) like the elastic field (phonons) and we can't quantize directly the EM-field tensor ...
3answers
421 views

### Why isn't light scattered through transparency?

I'm asking a question that has bothered me for years and years. First of all, let me give some context. I'm a layman in physics (college educated, math major). I've read Feynman's QED cover to cover, ...
1answer
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### Relativistic corrections to quantum mechanics of Coloumb potential

Systems of charged particles (such as atomic nuclei and electrons) can be described by nonrelativistic quantum mechanics with the Coloumb interaction potential. A fully relativistic description is ...
2answers
728 views

### Bound states in QED

I am a beginner in QED and QFT. What is known (or expected to be) about bound states in QED? As far as I understand, in non-relativistic QM electron and positron can form a bound state. Should it be ...
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### Effect of introducing magnetic charge on use of vector potential

It is well known that Maxwell equations can be made symmetric w.r.t. $E$ and $B$ by introducing non-zero magnetic charge density/flux. In this case we have $div B = \rho_m$, where $\rho_m$ is a ...
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### Did the Feynman heuristic of “simple effects have simple causes” fail for spin statistics?

Someone here recently noted that "The spin-statistics thing isn't a problem, it is a theorem (a demonstrably valid proposition), and it shouldn't be addressed, it should be understood and celebrated." ...
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### Simulation of QED

Can anyone point me to a paper dealing with simulation of QED or the Standard Model in general? I will particularly appreciate a review paper.
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### How are classical optics phenomena explained in QED (color)?

How is the following classical optics phenomenon explained in quantum electrodynamics? Color According to Schroedinger's model of the atom, only particular colors are emitted depending on the type ...
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### Magnetic monopole and electromagnetic field quantization procedure

From the Maxwell's equations point of view, existence of magnetic monopole leads to unsuitability of the introduction of vector potential as $\vec B = \operatorname{rot}\vec A$. As a result, it was ...
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### What is the massless limit of massive electromagnetism?

Consider electromagnetism, an abelian gauge theory, with a massive photon. Is the massless limit equal to electromagnetism? What does it happen at the quantum level with the extra degree of freedom? ...
2answers
349 views

### critical electric field that spontaneously generates real pairs

With the current QED framework, If an electric field is strong enough (say, near a nucleus with $Z > 140$) , pair production will occur spontaneously? Is this a real effect or an artifact before ...
2answers
468 views

### Deriving Planck's radiation law from microscopic considerations?

In the usual derivation of Planck's radiation law, the energies or frequencies $\omega$ of the oscillators depend on the measurements $L$ of the black body. The model is such that the only ...
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### Why is the spinor field anti-commutator not made gauge invariant?

When we introduce minimal coupling for the Dirac spinor field, we introduce terms into the Lagrangian, by the substitution \$i\frac{\partial}{\partial x^\mu}\mapsto i\frac{\partial}{\partial ...
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### Can a photon exhibit multiple frequencies?

Can a photon be a superposition of multiple frequency states? Kind of similar to how an electron can be a superposition of multiple spin states.
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### Is there a simple way to compute some physical constant from Feynman diagram statistics?

I've been playing around writing some software to generate Feynman diagrams for QED, respecting the vertex "rules" described here, and avoiding creating isomorphic duplicates. So from a starter ...
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### How do electrons interact if one of them had just exited the two slits of the double-slit experiment?

Consider the following experiment: a double-slit set-up for firing electrons one at a time. Let's now add a second electron (orange), which is fired parallel to the first one, but in the opposite ...
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### Is there a strong force analog to magnetic fields?

In special relativity, magnetism can be re-interpreted as an aspect of how electric charges interact when viewed from different inertial frames. Color charge is more complex than electric charge, but ...
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### Where is the velocity term in Dirac current hiding?

The dirac current is $$J^\mu = \bar{\psi}\gamma^\mu \psi$$ It looks weird at first because there is no derivative in the expression. So the velocity must be hidden somewhere in either $\gamma$ or ...
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### How does charge work if photons are neutral?

How can an electron distinguish between another electron and a positron? They use photons as exchange particles and photons are neutral, so how does it know to repel or attract?
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### Properties of the photon: Electric and Magnetic field components

Consider an electromagnetic wave of frequency $\nu$ interacting with a stationary charge placed at point $x$. My question concerns the consistency of two equally valid quantum-mechanical descriptions ...
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### How to quantize the free electro-magnetic field in 2d?

I am wondering how one can quantize the free electro-magnetic field in the two dimensional space-time. The standard method of fixing the Coulomb gauge in 4d does not seem to generalize immediately to ...
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617 views

### EM wave function & photon wavefunction

According to this review Photon wave function. Iwo Bialynicki-Birula. Progress in Optics 36 V (1996), pp. 245-294. arXiv:quant-ph/0508202, a classical EM plane wavefunction is a wavefunction (in ...
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### Database of scattering amplitudes

I want to check whether my result for the invariant amplitude of the electron-electron scattering (to lowest order in $\alpha$; t+u channels) is correct or not. I can't find any reference that has ...
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### Geometrical significance of gauge invariance of the QED Lagrangian

The QED Lagrangian is invariant under $\psi(x) \to e^{i\alpha(x)} \psi (x)$, $A_{\mu} \to A_{\mu}- \frac{1}{e}\partial_{\mu}\alpha(x)$. What is the geometric significance of this result? Also why is ...
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### Is there Pair production in between charged plates

In classical electromagnetic theory, If parallel plates are charged oppositely and placed close to each other, there will be no charge will not flow from one plate to another. How does this situation ...
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428 views

### How is the path integral for light explained, or how does it arise?

In a question titled How are classical optics phenomena explained in QED (Snell's law)? Marek talked about the probability amplitude for photons of a given path. He said that it was $\exp(iKL)$, and ...
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### On Electromagnetic Self Energy

In the process of pair annihilation an electron and a positron annihilate each other to produce a pair of photons, conserving momentum and energy. As the oppositely charged particles approach each ...
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### Representation of phase in quantum mechanics

[Note: My discussion of the three answers can be found just after the question.] Imagine three points in space that differ only by a phase angle of "something" (what doesn't really matter). One way ...
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### Can a photon see ghosts?

Does it make sense to introduce Faddeev–Popov ghost fields for abelian gauge field theories? Wikipedia says the coupling term in the Lagrangian "doesn't have any effect", but I don't really know ...
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### Why are geons unstable? Are there other problems with geons?

I read in various places geons are "generally considered unstable." Why? How solid is this reasoning? Is the reason geons are not studied much anymore because we can't make more progress without ...
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### Why is the Gupta-Bleuler gauge unfashionable?

In the early days of quantum electrodynamics, the most popular gauge chosen was the Gupta-Bleuler gauge stating that for physical states, $$\langle \chi | \partial^\mu A_\mu | \psi \rangle = 0.$$ ...
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### How to calculate the properties of Photon-Quasiparticles

in recent questions like "How are classical optics phenomena explained in QED (Snell's law)?" and "Do photons gain mass when they travel through glass?" we could learn something about effective ...
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### How can an asymptotic expansion give an extremely accurate predication, as in QED?

What is the meaning of "twenty digits accuracy" of certain QED calculations? If I take too little loops, or too many of them, the result won't be as accurate, so do people stop adding loops when the ...
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### Is diffraction affected by interaction between photons and electrons?

Suppose we take a sheet of ordinary metal, make a narrow slit in it, and shine a light beam through the slit onto a screen. The light beam will diffract from the edges of the slit and spread out onto ...
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### Is it true that the angular momentum of electromagnetic waves in an anisotropic medium is an integral of motion?

Extending my previous question Angular moment and EM wave, does it make sense to talk about the angular momentum of electromagnetic waves in an anisotropic medium? It is not obvious that the angular ...
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### Why can't fermions be affected by effective gravity in non-linear quantum electrodynamics?

Quantum electrodynamics based upon Euler-Heisenberg or Born-Infeld Lagrangians predict photons to move according to an effective metric which is dependent on the background electromagnetic field. In ...
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### Do EM waves transmit spin polarization?

Suppose you have a normal dipole antennae (transmitter and receiver) . Spin polarized current (as opposed to normal current) is sent into the transmitter, it emits an EM wave and the Receiver receives ...
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