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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Magnetic monopole and electromagnetic field quantization procedure

From the Maxwell's equations point of view, existence of magnetic monopole leads to unsuitability of the introduction of vector potential as $\vec B = \operatorname{rot}\vec A$. As a result, it was ...
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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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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 very strong fields are required for a photon to split?

Photon splitting does not occur in free space as energy and momentum cannot be conserved in any Lorentz frame. But it does occur in the presence of a strong field. Consider the example of a Magnetar. ...
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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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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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151 views

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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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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Thomson scattering on the elections does not produce any circular polarization?

All references on CMB polarization has this statement as if it is a trivial fact. But I have to admit that I completely don't understand what this sentence is telling us.
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What is the phase space for outgoing photons?

For a scattering process for which $n$ fermions are scattered, (by some conventions) the cross section acquires a phase space factor of: $$d\sigma \sim \prod_{i=1}^n\frac{d^3p_i}{(2\pi)^3 2E_i}$$ ...
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176 views

Double Slit Experiment with Two Independent Sources

Imagine a variation on the double slit experiment. I'll describe it in 2D using the $x-y$ plane. The $x$-axis is impenetrable other than the two slits, which are positioned at $(-1,0)$ and $(+1,0)$. ...
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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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experiment proposal to validate microcausality

I've been wondering about microcausality for some time now (a recent question of mine regarding the topic) and i'm wondering if its possible to devise an experiment to detect potential violations I ...
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174 views

Transition of electric charge to “magnetic charge” when $\alpha$ gets >> 1 in QED?

I`ve just learned that electrically charged particles and magnetically charged monopoles in QED are S-dual to each other such that it depends on the value of the fine structure constant which of the ...
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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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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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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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68 views

Time ordering, interaction Lagrangian calculation, QED

I am trying to compute $$ \langle 0| \, T\left\{\phi^\dagger(x_1) \phi(x_2) \exp \left[i \! \int{L_1(x) \, \mathrm{d}x} \right] \right\}|0 \rangle $$ for $$ L_1(x) = ...
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Intuition behind $U(1)$-gauge model of Electrodynamics in a general spacetime

As the article Electrodynamics in general spacetime greatly explains, the $U(1)$-gauge theory is a good base for working in non-simply connected spaces. But I wonder whether there is a deep reason to ...
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Non-minimal coupling (Pauli Coupling) of gauge field with a non-relativistic scalar field

I am wondering if it makes any sense to non-minimally (say, Pauli-like) couple an external gauge field with a non-relativistic scalar field: \begin{equation} p_\mu \rightarrow p_\mu - e A_\mu + ...
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Convergence of light by light scattering amplitude

Perhaps I'm too exhausted to see the answer of why the photon-photon scattering should contain no divergences. In Peskin and Schroeder page 320 we find that because of the Ward identity the ...
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Feynman propagator with general $\xi$ parameter

Hey from my notes in my PS book it seems I have solved this some time in the past, but I cannot seem to get the indices straight this time around. So in deriving the Feynman photon-propagator which ...
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Can the rate of virtual pair production from vacuum be computed?

Consider for instance the QED Lagrangian. Is it possible to compute the rate of virtual electron-positron creation from the vacuum?
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Expectation value for the time of a photon reflection

A photon is reflected by matter (by an electron in empty space). How long does the reflection take? (i.e. is there any infinitesimal time elapsing during the reflection process?), or more precisely, ...
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110 views

Vector potential and gauge in electromagnetism

In a paper by Zimmerman [JOURNAL OF APPLIED PHYSICS 114, 044907 (2013)], it is stated that the Lorenz gauge in electromagnetism is the only gauge with real physical meaning. How do I reconcile this ...
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Electromagnetic force interaction

As far as I know, the electromagnetic force only interacts on particles with electrical charge, but I was told that the electromagnetic force was involved in the following reaction: ...
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Electron propagator in a strong background B field

Near a magnetar with $B>B_\rm{QED}$, the strong B field will suppress the Compton scattering cross section of photons with a specific polarization (E-mode). Some references I know deal this problem ...
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Difference between positron and electron scattering in Coulomb field

In first order of perturbation theory the S-matrix amplitude for electron scattering in the Coulomb field will be (up to normalization factors) $$ S_{fi} = \frac{iZ q^2}{\sqrt{2E_{f}2E_{i}}}\bar ...
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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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If the measurement of the proton size is correct and it is lower that it was expected than what are the theoretical implications?

In the press release of the recent measurement of the proton structure, they barely mention various theoretical explanations for the effect. What is the most likely (not assuming now that the ...
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How does this paper relate to standard QED?

This paper proposes a microscopic mechanism for generating the values of $c, \epsilon_0, \mu_0$. They state that their vacuum is assumed to contain ephemeral (meaning existing within the limits of ...
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Nonlinear refraction index of vacuum above Schwinger limit

This question is more about trying to feel the waters in our current abilities to compute (or roughly estimate) the refraction index of vacuum, specifically when high numbers of electromagnetic quanta ...
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After quantization of electron vibrations, do we need electrons anyway?

The title question is not ment in a general context, but one in which goes to the plasmon theory. In that case, how is are the statistics (boson vs. fermions) of plasmons determined? And is there an ...
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Quantising the magnetic monopoles the make Maxwell symmetric

I don't believe this has already been asked, but I might be wrong; sorry. One can add a magnetic charge density/magnetic monopoles to Maxwell's equations to make the theory symmetric between the ...
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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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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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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 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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Energy conservation if photon absorbed below resonance

Suppose I have some quantum system (like atom) with excitation energy $E_{exc}$ which is homogeneously broadened due to finite lifetime. I shine light with narrow spectrum centred around energy ...
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Invariance of the QED Lagrangian under charge conjugation

Is it true that the QED Lagrangian $$\mathcal{L} = \bar{\psi}(i\gamma^\mu D_\mu-m) \psi $$ is invariant under charge conjugation? $$\begin{align} \psi &\mapsto -i(\gamma^0 \gamma^2 \psi)^T\\ ...
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Charge dependence of operators in QED renormalization

Consider a UV cutoff regulator $\Lambda$ with an effective QED lagrangian: $\mathcal{L}_{\Lambda} = \bar{\psi}_{\Lambda}(i\not \partial - m_{\Lambda})\psi_{\Lambda} - ...
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Electric field due to rotating charged sphere

Consider a spherically symmetric charged object (charge $Q$) rotating about its axis. From Gauss's law we know that all that matters for the electric field $\mathbf{E}$ is the charge $Q$ enclosed ...
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Differential cross section for photon scattering on fixed magnetic dipole

Photon with energy $\hbar\omega$ scattering on a fixed particle with magnetic momentum $\vec{\mu} = \mu \vec s$. How to calculate a differential and total cross section for the photon. I've found in ...
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Can a quark irreversibly pass though an event horizon?

This is an attempt to transform a question I asked about a year ago into a binary yes-or-no question: Since a quark has electrical charge, can it irreversibly pass though an event horizon? The ...
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One loop correction to $F^2$ in massless QED, question from Peskin & Schroeder

In Peskin & Schroeder chapter 19, about trace anomaly in massless QED, the trace of $\Theta^{\mu\nu}$ is given by $$ {\Theta^\mu} _\mu =-\frac{4-d}{4} (F_{\lambda\sigma})^2 + (1-d) \bar{\psi} i ...
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Can the diffraction/interference pattern behind the slit (double slit) be calculated with Feynman path integrals (QED)?

I often see Feynman path integrals explained by a graphic which shows the slit and then the electron goes all possible ways behind the slit. Ok that is nice to understand the Feynman path integral, ...
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Why is the Higgs mass renormalization considered a fine-tuning problem, while the electron mass (in QED) isn't?

Don't both masses require infinite corrections in their renormalization procedure? It is my understanding that the electron self-energy in QED increases to infinity with increasing cutoff value on ...