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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Can an Electromagnetic Gauge Transformation be Imaginary?

The Hamiltonian of a non-relativistic charged particle in a magnetic field is $$\hat{H}~=~\frac{1}{2m} \left[\frac{\hbar}{i}\vec\nabla - \frac{q}{c}\vec A\right]^2$$. Under a gauge transformation ...
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How does one show using QED that same/opposite electric charges repel/attract each other, respectively?

Why do same charges repel each other and opposite charges attract each other (please explain the phenomenon using real laws of nature (QED) not with the approximation model)?
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What's the relation between virtual photons and electromagnetic potentials?

Given that: 1) virtual photons mediate the electric and magnetic force fields 2) the magnetic field is the curl of the magnetic vector potential 3) the electric field is the negative gradient of ...
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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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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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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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Box normalization

Whenever we study free fields, the solutions of these fields (or particles, whatever feels most comfortable) are always given by plane waves. The dispersion-relation $\omega=\omega(k)$ will of course ...
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Charge Renormalization and Photon Propagator

I'm trying to understand charge renormalization in QED. I know that one can write the full photon propagator as $$\frac{-i\eta_{\mu\nu}}{q^2(1-\Pi(q^2))}$$ where $\Pi$ is regular at $0$. Obviously ...
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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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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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Is the third spin vector of a photon always suppressed?

I like to tell people interested in light polarization that the photon is a vector boson for which the third spin axis, the one in the direction of travel, is suppressed due to photons being massless ...
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Gauge Field Tensor from Wilson Loop

It is possible to introduce the gauge field in a QFT purely on geometric arguments. For simplicity, consider QED, only starting with fermions, and seeing how the gauge field naturally emerges. The ...
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Some questions about Ward-Takahashi Identity

I'm a learner of Peskin and Schroeder's textbook of quantum field theory. I have proceeded to Ward-Takahashi identity and have one question when I look for Wikipedia for reference. The following is ...
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Do virtual photons have a frequency?

Real photons do have frequencies, which is directly related to its energy. So, can virtual photons that take part in EM interactions have frequencies too? When my hand is pressed up against a glass ...
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Determinant of Dirac operator in flat space?

How would you evaluate \begin{equation}|iD\!\!\!\!/-m|\end{equation} Where $D_{\mu}=\partial_{\mu}-ieA_{\mu}$. I have an idea of how to do this without the gauge field, because it's essentially ...
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Does QED provide a closed form for Coulomb logarithms?

The classical models for the integrand as well as the cut-offs in computing the Coulomb logarithm are pretty rough. Does quantum electrodynamics have definite expressions for the quantity ...
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Integration & bremsstrahlung calculation

In this paper (relevant pdf section) that I'm reading, involving the calculation of bremsstrahlung in electron proton scattering (diagram below), the author calculates the integral over outgoing ...
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Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory

Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument: ... With a generalization of the argument given there (section ...
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Why aren't all photons virtual particles even in the “vacuum” of empty space? [duplicate]

I'm thoroughly confused about the nature of electromagnetic radiation. Light is supposed to exhibit both wave and particle characteristics. But does that mean that it is both a wave and a particle or ...
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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? ...
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Radiative Corrections and Bremsstrahlung

I am having trouble understanding why it is consistent to include "Breamsstrahlung" diagrams in computations of scattering amplitudes. For example, consider the scattering of two electrons to two ...
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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 ...
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Virtual photon counting

How to calculate number of exchanged virtual photons per unit of time between two electromagnetically interacting objects?
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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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Why and how, in QED, can excited atoms emit photons?

The quantum mechanics of the structure of atoms as determined by the electromagnetic forces inside them correctly describes the location and coupling of the different energy levels in essentially all ...
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Gauge choice after Spontaneous Symmetry Breaking

After the spontaneous breakdown of local symmetry in presence of gauge fields (Higgs Mechanism), we can always choose a gauge where the Goldstone bosons are eaten up by the gauge field (also called ...
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Is forward scattering = no scattering?

What is forward scattering? If it is equivalent to no scattering, then why not call it "no scattering"?
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No non-trivial UV asymptotically free and IR free

How it could be proven that a non-trivial theory cannot be both asymptotically free and IR free (g=0 both in the UV and IR with some interpolating function in between)? This is of course contrary to ...
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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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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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Mass gap for photons

I am puzzled by the answers to the question: What is a mass gap? There, Ron Maimon's answer gives a clear-cut definition, which I suppose applies to any quantum field theory with Hamiltonian $H$, ...
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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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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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Mass corrections to fermions proportional to the mass?

In this post regarding quantum corrections to a massless fermion field, the answerer stated that quantum corrections to the mass will always be proportional to the mass (at least in QED). This point ...
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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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Quantum Electrodynamics

I was wondering if anyone could give a simple explanation of how light interacts with matter. From what I have read in QED, electrons will repel each other because of their ability to emit and ...
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Ward Identity makes QED logarithmic divergent?

Quick question regarding superficial degrees of freedom and Ward identities. For instance in Peskin and Schroeder it is stated that the photon-self energy is superficially quadratically UV divergent ...
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Maxwell's equations in microscopic and macroscopic forms, and quantization

The macroscopic Maxwell's equations can be put in terms of differential forms as $$\mathrm{d}\mathrm{F}=0,\quad\delta \mathrm{D}=j\implies \delta j=0,\quad \mathrm{D}=\mathrm{F}+\mathrm{P}.$$ ...
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Why is it important that the vector current should be conserved in QED?

In Quantum Field Theory and the Standard Model by MD Schwartz in the chapter about the anomalies, he derives from the equation of motions and the Noether currents of a effective massless QED ...
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Is the gauge fixing $\partial_\mu A^\mu + \gamma A_\mu A^\mu=0$ used in the literature and does it have a name?

In an exercise for a course on Gauge Theories, I was asked to derive the action of QED with the method by Faddeev and Popov, using the following gauge-fixing function: $$F(A) = \partial_\mu A^\mu + ...
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How do non-transverse photon polarizations cancel in Euclidean QED?

First, recall how to write scattering amplitudes in covariant fashion in Minkowskian QED. One starts by considering some process with an external photon whose momentum is chosen to be ...
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How do fermion and scalar masses run with energy? Is the difference in their running the core of the hierarchy problem?

Do fermion and scalar running masses run in the same way? Specifically, what are the qualitative differences in the mass beta functions for, say, scalar $\lambda\phi^4$ field theory and the fermion ...
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What happens to Hydrogen-Boron plasma at 3 billion Kelvin?

A recent popular report states (beware, I believe it is not peer reviewed and this slightly smells like a PR stunt) that a private company TriAlpha has made some notable progress towards ...
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gauge invariance of the Feynman amplitudes

When we calculate the photon polarization sums over amplitudes, $$X=\sum\limits_{r=1}^{2}|\mathcal M_r|^2=\mathcal M_\alpha\mathcal M_\beta^*\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta$$ ...
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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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Why can't Compton scattering happen in leading order of perturbation theory?

Why is the matrix element of Compton scattering in leading order of perturbation theory equal to zero? Why can this process only be described in second order of perturbation theory, i.e. with exchange ...
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Can a neutrino act as a virtual particle between two electrons to mediate an electron-electron fermonic interaction?

Can a neutrino act as a virtual particle between two electrons to mediate electron-electron fermonic interaction analogous to how a photon acts as a virtual particle between two electrons to mediate a ...
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If proton spin emergence from quarks and gluons is mysterious, why is silver atom spin not?

A recent Scientific American article brought up an old issue, which is this: According to quantum chromodynamic models, the emergence of exactly 1/2 unit of spin in a proton (or a neutron, or any ...
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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.