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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QED renormalization: mass and dirac field

Why the mass renormalization $Z_m$ and the field renormalization $Z_\psi$ in QED (MS-renormalized) does not contribute to the beta function computation? From Ward identity, I know that $Z_A=Z_e^{-1}$, ...
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What happens to theoretical physics if a photon has non-zero mass?

I want to know the theoretical implication if photons have a non-zero mass. What happens to the Maxwell equations? What happens to QFT? If the photon have mass it can decade?
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Phase on Aharonov-Bohm effect doubts

How I show that $$\Lambda(\textbf{x}')=\frac{q}{\hbar}\int \mathbf{A} \cdot d\mathbf{x'}$$ on $$ \tilde{\psi}(\textbf{x}',t)=e^{[\frac{iq\Lambda(\textbf{x}')}{\hbar c}]}\psi(\textbf{x}',t)$$ for ...
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Compton Scattering Feynman diagram integral expression

I'm trying to write down the integral expression according to the feynman-rules for this Diagram of an electron with compton scattering and a one-loop correction: ![Compton Scattering][1] ...
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Current density defined by the scattering operator

I have a problem with the definition of the current density. In most literature it is defined as $j^\mu=\frac{i}{2}(S^*\frac{\partial S(A)}{\partial A_\mu(x)})$. I understand that normally we use ...
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What is $\mathcal{N}=2$ QED?

I would like to know is $\mathcal{N}=2$ QED is simply a $\mathcal{N}=2$ theory with gauge group $U(1)$ like in normal QED? If not, exactly what theory is it? Is there some reference for it?
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Occurance and disappearance of degeneneracies in a periodic structure of (quantum) LC circuits

Introductory part I'm currently studying an analytical model of coupled LC circuits, in preparation for actually performing measurements on such structures. While the final goal will struggle with a ...
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54 views

Photon emission/absorption by an atom and local gauge invariance

I understand that the local gauge invariance leads to a photon emission/absorption when the phase of an electron field is changed while the amplitude being unchanged. I'd like to know whether this ...
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250 views

What creates voltage?

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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How sketch the renormalization group flows in the $(\lambda, e^2)$ plan for scalar QED?

I have obtained beta functions of renormalization group for scalar QED: $$ \beta (e) = \frac{e^3}{48 \pi^2} $$ $$ \beta(\lambda) = \frac{1}{24\pi^2}(5\lambda^2 - 18e^2\lambda + 54 e^4) $$ which give ...
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Why does accelerating electron emits photons? [duplicate]

I have read that accelerating or oscillating electron emits photons. But why and how does it so? And why only photons? There are other bosons like gluons, W and Z bosons, so why does electron emit ...
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Can we quantize Maxwell-Chern-Simon Theory through Gupta-Bleuler approach?

In 3+1 QED we covariant quantize the Maxwell theory through Gupta-Bleuler method. But I have seen that MCS theory is explicitly covariant quantized using Nakanishi auxiliary field. Why cannot we take ...
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Why is a transmon a charge qubit?

The classic charge qubit is the cooper pair box which is a capacitor in series with a Josephson junction. In my understanding, by changing the gate voltage at the capacitor, one can create a ...
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80 views

Deriving Coulomb's law from quantum electrodynamics [duplicate]

Is it possible to derive the Coulomb's law using the principles of quantum electrodynamics? How?
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80 views

Deriving solution of the Renormalization Group Equation

I am trying to follow Matthew Schwartz's renormalization group lectures (pdf or see Chapter 23 of QFT and the SM by Matthew Schwartz), but I am having trouble with Eq. (book 23.31/pdf 29). I ...
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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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Integration for quantum amplitude of the coupling between two molecules

I am trying to solve following expression for quantum amplitude of coupling between two molecules, (arriving from the second order perubation) $$\frac{1}{p}\nabla_{j}\int e^{ipR\cos(\theta)} dT=i\int ...
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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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Massive vector field in curved spacetime

Setup Consider a massive vector field in anti-de Sitter space AdS$_{d+1}$ with metric $$ ds^2=\frac{1}{z^2}\left(dx_\mu dx^\mu+dz^2\right) $$ where $dx_\mu dx^\mu$ is the line element in d+1 ...
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Fastest path of light [duplicate]

Fermat's principle of least time says that light always takes the fastest path to any point. So how can light know which is the fastest path without taking all the paths first?
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Scalar QED perturbation theory [closed]

Where can I find material about scalar QED? Renormalization, scattering matrix, perturbation theory, etc...
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14 views

Associated photon field of a two state system

Given the time-dependent density matrix $\rho(t)$ of a driven two-state system $\mathcal{S}$. How do I calculate the time-dependent quantized photon field that would be generated by transitions in ...
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Correction to the residue in QED using $\overline{MS}$ contains IR divergence

I'm Calculating the next-to-leading orders in QED, but I'm using $\overline{MS}$ scheme, as known in $\overline{MS}$ the residue is no longer one and I have to calculate the correction to the residue ...
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109 views

Can photons travel faster than $c$? (Feynman Lectures)

I apologise for the very non-technical nature of this question. I am new to QED and perhaps am interpreting things in the wrong way, but I'll ask anyway, and hopefully someone can provide a ...
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Maximum Power transmitted using General Relativity waves - cf Schwinger limit

In Electromagnetism, QED says that the linearity of Maxwell's equations comes to an end when field strengths approach the Schwinger limit. Its about 10^18 V/m. What is the corresponding formula for ...
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Does Fermat's principle of least time apply to sound waves?

I am reading Feynman's presentation of Fermat's Principle of Least Time, which explains the behavior of light; does it apply to waves in general? for example sound waves or waves on the surface of ...
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73 views

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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Quantum mechanics question in derivation of Heisenberg-Euler Lagrangian in Schwartz “QFT” notes

In http://isites.harvard.edu/fs/docs/icb.topic1246957.files/IV-9-EffectiveActions.pdf (Page 20) Schwartz derives the Heisenberg-Euler Lagrangian using Schwinger's proper time method. To do so, he ...
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48 views

Aharonov-Bohm experiment: A possible way to understand potentials?

I'm posting this question as a function of an another question I found here: What is potential energy truly? The answer of WetSavannaAnimal aka Rod Vance. As I understand the hole point is to see ...
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78 views

First-order EM Feynman diagram?

Is there any 1st order electromagnetic Feynman diagram? I.e. a process whose probability is just $\propto \alpha_{EM}$? If not, is there any physical reason why? We always need at least two particles ...
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383 views

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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36 views

How do logarithms show up in the one loop calculation of the vacuum polarization in QED?

I am following Peskin with the computation of the vacuum polarization in QED and there is one thing I do not see. Equation (7.90) reads ...
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The Schwinger Limit and the Breit-Wheeler Process

The Breit-Wheeler process requires a two photon system to have a total energy of at least twice the rest mass of an electron, which is determined by the frequencies of the photons. The Schwinger ...
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Why do Lorentz invariance and Ward identities imply the structure $\Pi(k^2)(k^2\eta^{\mu\nu}-k^{\mu}k^{\nu})$ for the photon self energy?

In the first page of this link we can read that Ward identities and Lorentz invariance make the form if the photon self-energy be $$\Sigma^{\mu\nu}=\Pi(k^2)(k^2\eta^{\mu\nu}-k^{\mu}k^{\nu}).$$ Why?
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Vacuum has zero spin in Dirac theory

I have troubles trying to prove a statement made by Peskin-Schroeder in page 61, section 3.5 where he says that the "spin" operator $J_z$ given by the non numbered equation $$ J_z= \int d^3 x ...
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Propagation speed of photons when taking higher-order QFT corrections into account

In our group of experimental physicist who have nothing to do with and know very little about quantum field theory, we recently had a question concerning the propagation speed of photons in vacuum: ...
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In an electron-positron annihilation, in what direction are the photons released?

I read that, in an electron-positron annihilation, at least 2 photons are produced, because of the law of conservation of momentum. my question is: in what direction are those photons released? and ...
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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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Feynman Diagram in QED non relativistic limit

I am following Peskin to read Feynman diagram. But in this image given, he used the non-relativistic limit to write the incoming fermion gamma mu product. How did he get it? Any explanations in ...
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Photon propagator inverse

If i have the operator $D^{\mu\nu}=\partial^{\mu}\partial^{\nu}+m\epsilon^{\mu\alpha\nu}\partial_{\alpha}$. What's your inverse $(D^{\mu\nu})^{-1}$?
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How to count the number of modes/polarizations of a Gaussian field theory?

A Gaussian (free) field theory is described by a quadratic action of the field, e.g. $S=\int\psi^\dagger K\psi$ (or $S=\frac{1}{2}\int\phi^\intercal K\phi$ for real fields). Usually one just need to ...
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How are (semi-) static fields treated quantum-mechanically?

I am trying to understand a seemingly paradoxical assertion in this answer which argues that the magnetic field of an inductor corresponds to virtual photons because there is no net momentum ...
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Models of light

As far as I'm aware, there are two different (and almost contradictory) models that describe the behavior of light: light as a wave (EM), and light as a particle (QM). From what I've heard, depending ...
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Why most of physics is somehow related to light? [closed]

It seems that for the past 200 years, every physicist is concerned about light. For example : Newton's particle model, Young experiment, Photo-Electrict effect and Einstein's formula, Special ...
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How does the electric field operator change inside an optical cavity

In the free field, transverse electric field operator is given by the below expression; $$d^{\bot}(R)=i \sum_{p,\lambda}\Big( \frac{\hbar cq}{2V\epsilon_{0}}\Big)^{1/2} ...
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Which of the following produces more current? [closed]

In (1) photoelectric effect, (2) Compton effect, and (3) pair production, a beam of electrons are released. Out of Three Which produces More current? And How?
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How wrong are the classical Maxwell's equations (as compared to QED)?

Now, I don't really mean to say that Maxwell's equations are wrong. I know Maxwell's equations are very accurate when it comes to predicting physical phenomena, but going through high school and now ...
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Electric current $j^{\mu}$ in standard QED vs. scalar QED

The expression for the 4-current $j^{\mu}$ in standard QED is $$ e\bar{\Psi}\gamma^\mu\Psi $$ and $$ \frac{e}{2 i}(\psi^\dagger D^\mu \psi - (D^\mu \psi)^\dagger \psi) $$ in scalar QED. I ...
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What do the tensors here equal to?

In the process $$e^+e^- \rightarrow \gamma \gamma$$ for which the amplitude can be written as: $M= \epsilon^*_{1\nu}\epsilon^*_{2\mu}(A^{\mu\nu}+\tilde{A}^{\mu\nu})$, where $\epsilon_i$ is the ...
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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} + ...