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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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 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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The size of an electron

Considering that an electron is a quantized excitation of the Dirac field, why are there still discussions regarding the "size" of an electron? Isn't the "size" of an electron simply defined as the ...
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How is charge expressed?

I am happy with the concept of electrons interacting with each other through the emission and absorption of photons, but what I don't understand is how the negative charge on an electron is expressed ...
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Photons traveling backwards in time?

Imagine that two widely separated charged particles $A$ and $B$ exchange a photon. Because they are far apart one can imagine that there is a major contribution to the photon propagator that travels ...
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Derivative with respect to ${\not}{p}$

When studying renormalization of QED in standard textbooks, we typically encounter derivatives with respect to ${\not}{p}=p^\mu \gamma_\mu$, i.e., $\partial/\partial{\not}p$. As far as I understand, ...
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Classical EM neglects electron recoil?

Imagine two electrons $A$ and $B$ at rest. Electron $B$ is at a vertical distance $r$ above electron $A$. Let us assume that the electrons are constrained to move on horizontal rails. At time $t=0$ ...
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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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Scalar QED, are there any scalar-fermion vertices in this theory?

Consider QED with an additional charged (complex) scalar field, $\phi$:$$\require{cancel} \mathcal{L} = -{1\over4} F^{\mu\nu} F_{\mu\nu} + (D^\mu \phi)^*(D_\mu \phi) - \mu^2 \phi^* \phi - \overline{\...
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Help to understand vertex function

In Weinberg's book (the quantum theory of fields, volume 1, pag 446, equation (10.4.19) ) is stated that $\int \ dx \ dy \ dz \ exp(-i p x - ik y + i lz) \langle\Psi_0,T\{J^{\mu}(x)\Psi_n(y)\bar \...
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Equality of electric charges of all leptons

What does it precisely mean the often repeated statement that the electric charges of all leptons are the same. Let's consider QED with two leptons: electron and muon. The interaction part of the ...
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How to understand the QED, QCD and standard model Lagrangians? [closed]

How do you read the QED, QCD and standard model Lagrangians? What do all the symbols and tensors represent? And, how can you derive them by yourselves?
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Is it reasonable to interpret the Lamb shift as vacuum induced Stark shifts?

This is a pretty hand-wavy question about interpretation of the Lamb shift. I understand that one can calculate the Lamb shift diagrammatically to get an accurate result, but there exist "...
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When can photon field amplitudes be written as field operators?

Suppose I have some classical field equation for two photon fields with amplitudes $A_1(z),A_2(z)$ (plane waves) given as ${A}_1=\alpha f(A_1,A_2) \\ {{A}_2}=\beta g(A_1,A_2) $ Under what ...
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Why possibility for X-ray to excite inner electrons higher than outer electrons?

It seems X-ray absorption spectroscopy is usually ascribed to the interation between photons and inner electrons. Does it mean inner electrons are much preferred by X-ray photons to outer electrons? ...
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Can the Lamb shift be expressed in more-or-less closed form in terms of the renormalized 2-, 3-,…,n-point VEVs of QED?

I see here that there are three contributions to the Lamb shift, from vacuum polarization (-27 MHz), from electron mass renormalization(+1017 MHz), and from the anomalous magnetic moment (+68 MHz). ...
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Do free electrons really not interact with photons?

If free electrons don't interact with photons, why are free electrons accelerated by electromagnetic fields?
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What is going on in the photon-photon scattering Feynman diagram?

I understand the basic concepts of a Feynman diagram, but I don't get what is going on here. I have named the photons ABCD and the fermions 1234 for clarity. I'm going to assume that the vertical ...
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Could future experiments on “Gravitational Casimir Effect” confirm the existence of gravitons?

From Casimir effect, we know that when two plates are placed very close to each other in vacuum, they attract each other because the quantum fluctuations that press on the two plates' outer surfaces ...
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When does the concept of electric field in classical electrodynamics fail, and QED is needed?

It is really hard to find reference to when the traditional concept of electric wave, especially TEM wave, fails, and needs to be replaced by quantum electrodynamics. So when does the concept fail? ...
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QED: Would atoms without electrons be visible?

I have been reading a lot of QED books lately, and understand (as well as possible anyway) the interaction between electrons and photons. But I can't seem to get a clear indication of the interaction ...
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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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What is the physical process (if any) behind magnetic attraction?

I understand that the electromagnetic force can be described as the exchange of virtual photons. I also understand that it's possible for virtual photons, unlike their real counterparts, to have mass (...
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How photons can emerge quantized if their cause is continuous?

I know that photons are quantized, they are not continuous. But they are created by an accelerated charge. So how is it possible to have a quantized outcome from a symmetric continuous event? I mean ...
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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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Do we know why the field produced by charge extends to infinity?

Do we have any model to show why charge field or magnetic field extends till infinity. Edit: I agree that according to coulombs law $1/r^2$ cannot be 0 but do we know why this happens.I think I am ...
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Are atoms unstable in 4+1 dimensions when quantum mechanics is taken into account?

I understand that in 3+1 dimensions according to classical physics atoms should be unstable however atoms are stable in 3+1 dimensions because the behavior of atoms is governed by quantum physics ...
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What creates voltage? What causes electrons to move in a wire?

I was trying to break down how a transistor works to a friend, and I took a moment to think about electric current and voltages. I realised I do not understand where these phenomena come from. I ...
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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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$U(1){\times}U(1)$ local gauge invariance derivative

In QED and the basic Higgs mechanism, there is a local gauge transformation where a scalar field $\phi$ is transformed as: $e^{i\theta\eta(x)} \phi$ The partial derivative of this however makes the ...
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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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QED BRST Symmetry

This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim: "Consider QED ...
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Running coupling outside QFT

I'm reading about the running coupling in QCD. I understand the vacuum polarization and its consequences. Also I've read that you can find the same phenomenon on the strong interaction, giving us the ...
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Why is tree-level interaction between neutral scalar and photons non-renormalizable?

I've read that the decay of a neutral scalar particle into two photons, i.e., $$ S(p+q) \to \gamma(p) + \gamma(q) $$ can't happen via tree diagrams and instead is caused by loop diagrams (such as a ...
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How do you go from quantum electrodynamics to Maxwell's equations?

I've read and heard that quantum electrodynamics is more fundamental than maxwells equations. How do you go from quantum electrodynamics to Maxwell's equations?
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QED Commutation Relations Implications

In Brian Hatfield's book on QFT and Strings there is the following quote: In particular $$ [A_i (x,t), E_j(y,t)] = -i \delta_{ij}\delta(x-y) $$ implies that $$ [A_i(x,t),\nabla \cdot E(y,t)] = -...
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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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Does electric charge affect space time fabric?

I am confused with this question. Does electric charge affect the space time fabric? If so, why? Also if electric charge does not affect the space time fabric, how can we interpret the origin of the ...
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How does one interpret the Dirac equation with a self-field potential?

EVERY QFT text I've ever examined states that if there is an external vector potential, $A_\mu$, then one writes the Dirac eq.(or Klein-Gordon eq.) using a covariant derivative to include this U(1) ...
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Sign of momentum in fermion propagator

Thinking of a process like Compton scattering, where we have an electron as a propagator, I would typically write down the propagator as $$i \frac{\not q+m}{q^2-m^2}.$$ If I were to replace the ...
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What is the difference between QED and quantum optics?

What is the difference between QED and quantum optics? Once you have QED, you have not only the quantized EM field, but also the interaction between matter and the EM field. So, you should have ...
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Gauge invariance (QED)

In his book, the author says that according to the Feynman diagrams of this process in QED $$e^+ e^- \rightarrow \gamma \gamma,$$ gauge invariance requires that $$k_{1\nu}(A^{\mu\nu} + \tilde{A}^{\...
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What is the constraint on the Gauge Potential in the Covariant Gauges?

One of the most common gauges in QED computations are the $R_{\xi}$ gauges obtained by adding a term \begin{equation} -\frac{(\partial_\mu A^{\mu})^2}{2\xi} \end{equation} to the Lagrangian. ...
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If a photon's emission is detected is it real or virtual?

I understand that one can measure a single photon being absorbed using a photomultiplier tube or CCD. Can one measure a single photon being emitted by monitoring the current through an LED or the ...
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What are the limits of applicability of Coulomb's Law?

Coulomb's law is formally parallel to Newton's Law of Universal Gravitation, which is known to give way to General Relativity for very large masses. Does Coulomb's Law have any similar limits of ...
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Where does the mass term come from in the Proca Lagrangian?

There are many good books describing how to construct the Lagrangian for an electromagnetic field in a medium. $$ \mathcal{L}~=~-\frac{1}{16\pi}F^{\mu\nu}F_{\mu\nu}-\frac{1}{c}j^{\nu}A_{\nu} $$ ...
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What's the role of field equation in QFT?

For free field theory, it seems the solutions of a field equation are used to give a representation of Poincare group, and the field equation is still satisfied after quantization. However for an ...
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What is the QED model about half wave plate?

Surely classical electrodynamics (CED) has a good and well-known answer about the change of light polarization in a HWP (or Quarter wave plate). I tried to find how does this look like from point of ...
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Electromagnetic Field VS Photons [duplicate]

I am currently studying electrodynamics with all the fields and the like. Now, as I understand it, in a more modern viewpoint there is a duality between electromagnetic fields and photons, with ...
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What low-level process drives a frequency-doubling crystal?

I was reading about second-harmonic generation (SHG) crystals (or frequency-doubling crystals) used to produce green laser light from IR. What low-level process in the crystal is actually driving ...