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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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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How can results from classical optics be obtained from QFT?

Recently it came to my mind, that I have some basic knowledge about QFT and know im principle how to calculate scattering amplitudes (at least for the $\phi^4$-theory), but have no idea how to ...
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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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What is the 2-point correlation function of the electron field in QED?

The Feynman propagator for the free electron field is the Fourier transform w.r.t. $y$ of the time-ordered 2-point VEV $\left<0\right|\mathcal{T}[\hat\psi(x)\hat\psi(x+y)]\left|0\right>$, taking ...
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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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Why can't photons have a mass

Why can't photons have a mass? Could you explain this to me in a short and mathematical way?
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 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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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 the electron is point like, then what is the significance of the classical radius of the electron?

What is the physical meaning/significance of the classical radius of the electron if we know from experiments that the electron is point like? Is there similarly a classical radius of the photon? The ...
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The fine structure constant - can it genuinely be a random variable?

The question Does it make sense, and are there physical reasons to think about the fine structure constant as a (very concentrated) probability distribution rather than a single real number? ...
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How do you derive the Lagrangian for the Standard Model?

Is there a way to derive the Lagrangian for the Standard Model just like one would for Einstein's field equations for instance? Also, how do you derive the Laganrigans for QCD and QED? Is it possible ...
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Is there any idea why the electric charges of electron and muon are equal?

Is there any idea explaining why the electric charges of electron and muon are equal? Edit: The total charge of a particle is proportional to the integral of its own electric field flow through the ...
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Does the Casimir effect allow to change the lifetime of a radiating atom?

Is it true that a spontaneously light-emitting atom changes its lifetime if it is put between two parallel plates that are so near that they attract each other through the Casimir effect? Thus: does ...
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QED Vertex Factor/Rule

On page 303 in Peskin&Schroeder they give the vertex factor as $$V = -ie\gamma^\mu \int d^4x$$ while on page 304 they write $$V_\times = -ie\gamma^\mu\int d^4x A_\mu(x).$$ Why are the ...
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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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Vanishing of photon one-point function in QED

I would like to know why the photon one-point function vanishes in QED. I am aware that any $n$-point functions vanishes for odd $n$ because of 'charge-conjugate" argument, this does not apply to ...
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How many photons can an electron absorb and why?

How many photons can an electron absorb and why? Can all fundamental particles that can absorb photons absorb the same amount of photons and why? If we increase the velocity of a fundamental ...
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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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Is the fine structure constant actually a constant or does its value depend on the energy scale?

The value of the fine structure constant is given as $$ \alpha = \frac{e^2}{4\pi\varepsilon_0\hbar c} = \frac{1}{137.035\,999..} $$ It's value is only dependent on physical constants (the elementary ...
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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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Does light really “travel”?

From what I've so far understood about light, a photon is emitted somewhere and after some time it's absorbed somewhere else. Have we had experiments that confirm the path taken or something akin to ...