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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Charge operator for Dirac spinor

In QED, the gauge transformation which acts upon a fermionic field $\psi$ is $$\psi'(x)= e^{i \alpha(x) Q}\psi(x)$$ where $Q$ is the charge operator. Most of the time it's just written as $$\psi'(x)= ...
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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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How does light know which path is fastest?

We know from Fermat's principle of least time that light follows the fastest path. But how does light know which path is the fastest?
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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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Bound states in QED

I am a beginner in QED and QFT. What is known (or expected to be) about bound states in QED? As far as I understand, in non-relativistic QM electron and positron can form a bound state. Should it be ...
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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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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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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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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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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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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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Why Lagrangian of electromagnetism with Lorenz Gauge evolve Klein Gordon equation?

Simply Lagrangian without a source for Maxwell equation is $$ L = -\frac{1}{4}F^{\mu\nu}F_{\mu\nu} $$ Also Lorenz Gauge condition is $$ \partial_{\mu}A^{\mu}=0 $$ and if so I can briefly add this ...
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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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Does a quadrupole transition mean emission of one photon with spin 2?

If it's true and spin-2 photons do exist, could you please point to some literature that discusses spin-2 photons? If not, then how exactly does a selection rule for quadrupole transition make sense ...
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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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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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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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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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Isn't the Coulomb interaction a photon interaction between two charges?

Isn't the Coulomb interaction a photon interaction between two charges? if yes then what does the following text mean? (Many-particle Physics by Gerald D. Mahan.)
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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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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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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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How do I calculate a Feynman diagram with one loop?

I'm following Peskin & Schroeder and I'm trying to calculate the momentum space representation for the following diagram, Q4 in this link. Paper The loop is what's causing me problems. I'm not ...
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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 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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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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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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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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Can we measure the electron spin independently of its magnetic moment?

What experimental evidence do we have for the intrinsic angular momentum of the electron (its spin)? I am specifically interested in whether we have a value for this that is independent of 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} + ...
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What would the collision of two photons look like?

Could someone explain to me what the collision of two photons would look like? Will they behave like, Electromagnetic waves: they will interfere with each other and keep their wave nature Particles: ...
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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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Electron-positron scattering: why is this the only diagram?

This is probably a very basic question, but I've been going through all my course materials and looking through various books to find a simple way of figuring this out. But consider the following ...
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Can an electron which is a bound in an atom absorb more than one photon at the same time? [duplicate]

Can an electron which is a bound in an atom absorb more than one photon at the same time ? In specific during photo-electric emission can an electron take in more than one photon if one photon doesn't ...
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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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Is it possible to give photons an electric charge?

I know that photons have no electric charge and that they are stable, but is it possible to give them a positive or negative charge? If so how?
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Is there an expression for field charge analogous to field mass?

In electrodynamics, it is possible to derive an expression for the field momentum for a given moving charge distribution (e.g. a sphere with uniform velocity) and from that infer an "electromagnetic ...
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Is the elementary charge really a constant of nature? - Accuracy of QED

There are a couple of natural constants; examples are Planck's constant or the Speed of light in vacuum. The elementary Charge is the coupling factor to all Kind of electromagnetic interactions; this ...
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Physical meaning of the coupling matrix in Fermi golden rule

I am calculating the energy transfer rate using Fermi golden rule where the coupling matrix $M$ is obtained using second order pertubation method. $$ \Gamma_{tran}=\frac{2\pi}{\hslash}|M|^{2}\rho$$ ...
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How do photons mediate (or create) a force?

Is there a somewhat intuitive explanation as to why the exchange of a photon between two particles causes a force between those particles? Is there a difference in the way massless and massive ...