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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Does electron field exist?

We know, that one-particle states can be earned from relativistic fields, which can be interpreted as functions determined on Minkowski space-time. Field must satisfy some conditions, by which we ...
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Can a photon survive a collision? If so, is it at rest during the process?

Background Irving Kaplan, in Article 6.7: The Compton Effect of Nuclear Physics (2nd Ed.) explains the Compton effect as follows: Compton (1923) was able to show that when a beam of ...
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Virtual photons as force mediators in QED - really?

If the photon is the force vector for EM interactions, e.g. electrons, how does each electron 'know' where the other one is so that it can send it a photon? I've thought about this for a while. I ...
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Equivalence between different formulations of QED

I have looked at Greiner's book on QED, where he uses the Feynman propagator approach for QED. He solves a lot of things and calculates several processes without "second quantisation" (and without ...
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How to get Hamiltonian of QED from lagrangian?

I have the QED lagrangian: $$ L = \bar {\Psi}(i \gamma^{\mu }\partial_{\mu} + q\gamma^{\mu}A_{\mu} - m)\Psi + \frac{1}{16 \pi}F_{\alpha \beta}F^{\alpha \beta} . $$ I tried to get hamiltonian by ...
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Does the 4/3 problem of classical electromagnetism remain in quantum mechanics?

In Volume II Chapter 28 of the Feymann Lectures on Physics, Feynman discusses the infamous 4/3 problem of classical electromagnetism. Suppose you have a charged particle of radius $a$ and charge $q$ ...
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Dimensional transmutation in QED?

I am familiar with the QCD dimensional transmutation (QCD is dimensionless theory but via renormalisation we get dimensional parameter; we have to choose some referent scale...), but I'm not sure if ...
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Christoffel symbols and Dirac matrices mathematical similarities?

Maybe mine is a silly question, but are there mathematical similarities or common roots between the Christoffel symbols: $ \nabla - \partial = \Gamma $ and the Dirac matrices $ ( \gamma^\mu ...
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EMF induced in a dynamo is by photons of permanent magnets?

i know little about the quantum field theory and also that the permanent magnets have there fields because of exchange of virtual photons across or around the ends. so when we take a dynamo and the ...
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Coulomb interaction as virtual particles exchange?

I've been reading about virtual particle exchanges in physics books and in Physics SA posts, where a particle interpretation of gravity and Coulomb interaction is established. The Feynman Diagram ...
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accelerated charge in QED

Classical electromagnetism says an accelerated charge would radiate. Is this understood in QED? Is there QED derivation of Larmor's formula?
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Mass dimension of coupling constants in various dimensions

Just a quick question: Suppose I want to consider QED or YM in 4 dimensions we always say that the coupling constants are dimensionless and that the field then has a specific mass dimension. What ...
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taking the trace

could anyone show me the first couple of steps in taking the trace of something like this, im not sure how to start. 'Tr[$\gamma($$\gamma k + $$\gamma p + $$\gamma q + m) $$\gamma ($$\gamma k + ...
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Proof of Furry's theorem

i was wondering if anyone could give an explicit calculation or show a link that shows the proof to Furry's theorem. showing how the vacuum expectation value of any odd number of electromagnetic ...
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About the three point function at one loop order

Could someone explain how exactly do you calculate the trace of the three point function of one loop in QED. in the following link the expression from 1. a (2) ...
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How to derive the form of the parity operator acting on Lorentz spinors?

I'm reading Berestetskii (Volume 4 of Landau & Lifshitz) section 19 on inversion of spinors. Berestetskii says parity $P$ maps undotted spinors into dotted spinors and vice-versa as ...
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Magnetic monopoles in spin ice and Dirac string comparison

In spin ice systems magnetic monopole-like excitations are sources or sinks of $H$, not the $B$ field, why is that? Is it because the strings carries magnetic moment $M$ and not solenoidal $B$ filed ...
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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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The electron and classical dynamics

Can I use Newtonian laws of dynamics and kinematics applied to electrons (like $F = ma$ and $s = s_0 + v_0 t + at^2/2$)? If not, why not? I know that everything in principle behaves in a quantum ...
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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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LSZ theorem for photons

Is there any discussion on what the LSZ theorem for photons looks like? I would rather like a discussion of this in axial gauge $A_0 = 0$ (instead of the usual Lorenz gauge), but anything would do.
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Covariance of the Dirac equation and Infinitesimal Lorentz transformation

Okay, I've got really desperate now. I've spend 10 hours of work (for a few days) trying to prove 'trivial' equation in Quantum Electrodynamics. To anybody who want to write an answer for my questions ...
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Electron-Positron Scattering using the Feynman Rules - Integration Q

I'm doing independent studies on electron-positron scattering, specifically the annihilation diagram contribution to the M matrix in Bhabha scattering, and this is the equation I recovered with the ...
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Characteristic of photons for constant speed

What characteristic of photons causes them to travel with constant speed in all frames of reference? Till the topics I have studied, we always assume this but never got any ideas what can be in the ...
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How to verify gauge invariance of an amplitude

I have calculated a tree level amplitude for Compton scattering (${e\left(p\right)+\gamma\left(k\right)\to e\left(p\prime\right)+\gamma\left(k\prime\right)}$): $${ ...
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Is there any relationship between Gravity and Electromagnetism? [duplicate]

We all know that the universe is governed by four Fundamental Forces which are The strong force , The weak force , The electromagnetic force and The gravitational force . Now, is there any ...
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Some questions about virtual particles

When reading about quantum mechanics, I've stumbled upon a description of the force between two electrons as a result of virtual particles being "exchanged" by the two electrons. So far I've ...
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Conservation of BRST current in QED

I am trying to understand the conservation of the BRST current in QED but am having some trouble. This is what I have so far, QED lagrangian density in Lorenz gauge is, $$L = ...
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Evaluation of QED amplitude with 1 external photon

I'm trying to compute the exact QED amplitude with one external photon. Suppose that the photon has 4-momentum $q$ and polarization $\varepsilon^\mu$. Peskin and Schroeder (p318) claim that ignoring ...
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How do we know photons have spin 1?

Electrons have spin 1/2, and as they are charged, they also have an associated magnetic moment, which can be measured by an electron beam splitting up in an inhomogeneous magnetic field or through the ...
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How does the Ward-Takahashi Identity imply that non-transverse photons are unphysical in QED?

Peskin and Schroeder say that the Ward Identity of QED proves that non-transverse photon polarizations can be consistently ignored, but I'm confused about the details. Setup One starts by ...
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How to introduce the electromagnetic field in Quantum Field Theory?

There are many ways to introduce the electromagnrtic field in Quantum Field Theory(QFT), such as canonical quantization method which introduces the creation and annihilation oprators by treating 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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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 exactly is the connection between gauge transformations and symmetry groups?

For a given gauge transformation, say, the electromagnetic field, where observable quantities aren't affected by transformations of the form $$\mathbf{A}' = \mathbf{A} + \nabla \chi,$$ $$\phi' = \phi ...
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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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Negative mass dirac equation -> Propagator?

There are two types of dirac equations: $(p_\mu\gamma^\mu - m)\Psi(x) = 0$ and $(p_\mu\gamma^\mu + m)\Psi(x) = 0$. Here $p$ are the momentum operators. The fermion propagator is defined in the ...
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Understanding the argument that local U(1) leads to coupling of EM and matter

I'm trying to better understand the argument that U(1) local gauge invariance implies a coupling of EM and Dirac fields. I understand the math, but I'm not sure about the chain of logic. You start ...
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Why does positronium decay into 2 photons more often than into 3 photons?

I cannot find the answer to the above question. I know that para-positronium is created with a probability of $25\%$ and decays into 2 photons, while ortho-positronium is created with a probability ...
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'Validity' of QED/QCD/Electroweak interaction

I am currently attending a course on Quantum Field Theory and I got into thinking how valid these theories are. As the theory attempts to describe reality only far above the Planck (length) scale, ...
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Formula for Rabi frequency

I have calculated the dipole transition elements of electronic states $\langle a|D_1^m|b \rangle$ following the book of Cohen-Tannoudji (Complement $E_X$) and tried then to calculate from that the ...
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The divergence in QCD Series— How many are they, and what do they mean?

I am referring to this question, and especially this answer. In addition, QCD has - like all field theories - only an asymptotic perturbation series, which means that the series itself will ...
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Why electrons can't radiate in their atoms' orbits?

It's an old-new question (I found only one similar question with unsatisfactory (for me) answer: Where did Schrödinger solve the radiating problem of Bohr's model?) It's strange for me how all books ...
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Why do some materials reflect (metals) and other materials reflect and refract (glass) from the quantum perspective?

Recently I was asked to explain the difference between reflection and total internal reflection from a purely conceptual standpoint (no math). Let me explain what I already know. Reflection and ...
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Vacuum polarization in QCD and gluon bubbles

In analogy to QED, the following Feynman diagram is a diagram contributing to the vacuum polarization effect, leading to anti-screening, asymptotic freedom and running of the strong coupling constant. ...
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Fundamentals of Quantum Electrodynamics

In quantum electrodynamics, the classical Hamiltonian is obtained from the classical electromagnetic Lagrangian. Then the classical electric and magnetic fields are promoted to operators, as is the ...
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Electron in Magnetic Field can lead to non-Hermitian Hamiltonian?

Consider a charged quantum particle in a magnetic field. The Hamiltonian can be written using minimal coupling: $$ H = \frac{1}{2m} \left( \mathbf{p} - \frac{e}{c} \mathbf{A}(\mathbf{x}) \right)^2 $$ ...
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Photon detection time in NMR rotating frame

I think of an NMR experiment, but with a single spin half nucleus initially set to the excited state. When the nucleus finally returns to its ground state, it will emit a photon. An observer in the ...
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Charge in terms of wavefunctions

For a charged quantum particle, say, an electron or a quark, how in the particle's wavefunction is the electric charge represented? Is it truly possible to represent electric charge using the wave ...