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Questions tagged [quantum-electrodynamics]

Quantum electrodynamics (QED) is the quantum field theory believed to describe electromagnetic interaction. It is the simplest example of a quantum gauge theory, where the gauge group is abelian, U(1).

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Photon creation operator physical realization

I am trying to self study QED so I apologize if my question seems silly. As I realize, all physical processes should stem from some "hermitian" operator in the quantum language. As it is well known, ...
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Conservation of angular momentum in pair annihilation in scalar QED

Suppose we have the usual scalar QED for a massive charged field $\phi$ , $$\mathcal L=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+(D_\mu\phi)^\dagger(D^\mu\phi)-m^2\phi^\dagger\phi$$ with $g^{\mu\nu}=\text{...
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How to put the terms in correct order when deriving amplitudes in QED from the S-Matrix?

I am trying to derive the amplitude for the Møller scattering process $e^-+e^-\rightarrow e^-+e^-$ from "first principles", that is, by working out the calculation with the relevant S-matrix terms ...
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BRST Charge in QED

The pure gauge QED Lagrangian density, including the ghost fields, is \begin{align*} \mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}-\frac{1}{2\xi}(\partial^\mu A_\mu)^2+\partial^\mu\overline{c}\...
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atom Quantum electric electron [duplicate]

Hello can anyone tell me why we take Electric potential energy between oppositely charged particles negative. I know the formula but I need proper reasoning or its a convention . Actually I am taking ...
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The electric and magnetic field, reaching to infinity

I have difficulty’s to accept that the electric and magnetic field components of photons as well as of electrons and the other subatomic particles are extended to infinity. For practical use that does ...
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Proof relation expectation value (QED)

I am trying to prove the following relation $$ \langle\Phi|\hat{\bar{\psi}}(x)A\hat\psi(x)|\Phi\rangle=\bar\varphi(x)A\varphi(x)+\langle0|\hat{\bar{\psi}}(x)A\hat\psi(x)|0\rangle\,, $$ where $|\Phi\...
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Why does the Dirac equation work for the hydrogen atom?

The Dirac equation works well for predicting the spectrum of the hydrogen atom, famously incorporating relativistic effects like fine structure. Yet, there seems to be a sense in which this is ...
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What is the order of the number of significantly scattered particles in Møller scattering?

in an electron-electron collision with a low speed and in the nonrelativistic case, approximately what fraction of electrons get significantly deflected (say more than 10 degrees)? Generally, with ...
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How is the probability density for the deflection angle calculated from the differential cross-section?

In a scattering process, the probability density for the deflection angle of the incident particle is proportional to the differential cross-section of that scattering process. Given the differential ...
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What is electromagnetic radiation (when it is not a 'wave' of EM fields or interacting locally as a photon)?

My questions are related to the question asked at Are EM radiation and EM waves the same thing?. My background is in math (my Ph.D. thesis was in geometric analysis), and I have only taken basic ...
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single chirality electron and photon interaction

I asked a similar question about QED Lagrangian but I guess the question wasn't clear enough since I didn't get any correct answers. So, I'll try to ask the question in a different way: how does one ...
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What it means that there is only one electron in universe? [duplicate]

Could someone explain if this statement is and what could possible mean?
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QED Lagrangian in terms of Weyl spinors

Let's say the electron field can be written in term of its left and right handed Weyl spinors: \begin{equation} \psi_{e} = \begin{pmatrix} \chi \\ \eta^{\dagger} \end{pmatrix} \end{equation} In ...
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What is the fundamental difference between a cavity and plasmonic cavity?

In the process of exploring plasmonic systems I have quite often come across the description of cavities as Plasmonic cavities. What is the exact difference between a normal cavity and a plasmonic ...
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What is the Holo-Exchange symmetry of the tensor $\chi^{(2)}$?

In a paper by Lu-Ming Duan and Guang-Can Guo, they develop an alternative approach to quantising the EM field in a nonlinear and inhomogeneous media. In this derivation, they use the holo-exchange ...
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Mathematical bases/prerequisites for Feynman's “QED” [duplicate]

I have enjoyed studying Feynman's book "QED". I have sufficient mathematical maturity to go beyond his analogies. I am hoping someone has provided notes on the book enumerating the mathematical basis ...
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What quantum phenomena violate the superposition principle in electromagnetism?

On page 11 of the 3rd edition of Electricity and Magnetism by Edward M. Purcell and David J. Morin it says: "we know of quantum phenomena in the electromagnetic field that represents a failure of ...
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Spinless $e^{-}\gamma\rightarrow e^{-}$ Cross section

I was trying to figure out the cross section $\frac{d\sigma}{d\Omega}$ for spinless $e^{-}\gamma\rightarrow e^{-}$ scattering. First I wrote the terms associated with each component. Vertex: $$ie(...
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Stationary phase method for theories with both bosons and fermions

I am wondering if there exists a method to compute path integrals using the stationary phase method for theories with both bosons and fermions. (I am aware of such a method for theories with bosons ...
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Spatial wave-function of a single photon and its measurement

In the last decade there were several papers claiming that they've measured a "transverse quantum state" / "quantum wave-function" / "spatial Wigner function" of a single photon: Measurement of the ...
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What is the relationship between virtual photon flux/density and field strength

So if the electric field is transmitted via virtual photons I would assume there must a relation between the density/probability density function of virtual photons and the field strength. is this ...
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Does the electron act as point charge in scattering theory?

We know that an electron behaves like a point charge, and the probability density of its position is given by the Born rule. Now suppose that we shoot an electron toward an atom, so the electron gets ...
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Can an electron inside an atom annihilate? [duplicate]

We know that in QFT, all particles are being created and annihilated, and because of the conservation laws, on average the number of particles remains constant. Suppose we have an electron in an atom....
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When do we need fully quantum mechanically treatment of photon?

I'm wondering when do we need fully quantum mechanically treatment of photon.(i.e. quantized photon and quantum matter.) I kind of know that for sub-Poisson(photon statistics) light, fully quantum ...
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Question about field quantization

I'm reading a paper by Rubin, Klyshko, Shih and Sergienko titled "Theory of two-photon entanglement in type_II optical parametric down-conversion", 1994 (link to the paper). I'm stumped by equation ...
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What parameters determine the probability of virtual photon emission/absorption?

Suppose an electron is producing an electric field by emission of virtual photons and interacting with other particles. What parameters determine the probability that it will emit at least one virtual ...
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Can vacuum fluctuations change the position of an electron?

According to QFT, virtual electron-positron pairs are created everywhere in the space, and more frequently near electric charges. Suppose that one such a pair is created in the proximity of an ...
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What is the Energy of superfluidity helium liquid with momentum hk

I'm reading BK Agrawal Book. In chapter 24, Section 3 and 4 has been given about Interacting fermions and Bosons. Here in 3 Energy of Energies is given directly without any derivation and in 4 ...
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Topological theta-term as a background electric/magnetic field?

The topological $\theta$-term in the Schwinger model (1+1-dimensional QED) can be interpreted as a background electric field, as explained in Chapter 7.1.2 of Tong's lecture notes. The same holds true ...
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How does the electron know to “release” the photon at the same angle at which it got absorbed? [duplicate]

This is a quote from Wikipedia: In classical electrodynamics, light is considered as an electromagnetic wave, which is described by Maxwell's equations. Light waves incident on a material induce ...
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Do QED effects make a huge change to the position of the electrons?

In https://en.wikipedia.org/wiki/Lamb_shift about the lamb shift, it's mentioned that the change in the electron's frequency due to QED effects (vacuum polarization and self-energy correction) is ...
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What parameters determine the amount of Uehling potential and self-energy correction effects?

Uehling potential correction and electron self-energy correction are the two most important factors contributing to the lamb shift in the hydrogen atom, by "smearing" the wavefunction of the electron. ...
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Exact FRG flow equation for QED renormalizability proof

I would like to see how can one prove QED renormalizability in terms of Wetterich & Morris exact FRG flow equation for effective action $\Gamma_k$? May be my question is unclear.
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How does absorption of virtual photons “smear” a particle?

I have read that the electron self-energy correction, a process in which the electron absorbs a virtual photon, changes the position of the electron (which leads to the lamb shift in Hydrogen-like ...
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Does the Compton wavelength put a limitation on how precise we can measure the position of a particle?

I have read on Wikipedia (https://en.wikipedia.org/wiki/Compton_wavelength) that we cannot measure the position of a particle more precise than half of its Compton wavelength, since the photon we ...
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Conservation of $\int |\psi|^2$ for Dirac wave

When $\psi$ be Schrodinger wave $\int |\psi|^2$ is conserved even when this wave interact whit another wave say electromagnetic wave. and this is very necessary for one particle interpretation of this ...
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Relation between the trace anomaly and the energy-momentum tensor being off-shell

Let's say we have a massless QED theory with a Lagrangian \begin{equation} L=i\bar{\psi}\not{D}\psi-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} \end{equation} The symmetric energy-momentum tensor is \begin{...
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Is the direction of the Coulomb force at short distances indeterministic?

Suppose we have two electrons that apply a Coulomb force on each other. At large distances, we can consider the two electrons as point charges and the direction of the Coulomb force would be on the ...
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Is there any Bohmian approach to quantum electrodynamics?

I know that in some Bohmian papers (like https://arxiv.org/abs/quant-ph/0303156), electron-positron pair creation and annihilation is modeled by different methods like stochastic jumps in the ...
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Is the whole electromagnetic spectrum made of quanta?

My question is probably stupid (and maybe has already been answered on other posts), but I just started investigating quantum physics and I am struggling to understand the real meaning of "quantum". ...
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What is the physical interpretation of the derivative of a particle field?

I am learning quantum field theory, specifically the quantization of the electromagnetic field. We have this Laplacian $$ \mathcal{L} = -\frac{1}{2} \partial_\mu A_\nu \partial^\mu A^\nu -j_\mu A^\mu $...
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Sum over real photon polarizations. The minus sign

Ok for real photons there is the formula when summing over the polarizations: $$ \sum_{\lambda=\pm}\epsilon^{*\mu}_\lambda\epsilon^\nu_\lambda = -\eta^{\mu\nu}$$ But if I have a matrix element of ...
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Explanation about light reflection in Feynman's QED

In his book QED, Feynman explained how the probability of light reflecting from a mirror can be calculated by summing unit vectors, with their direction representing the phase of the wavefunctions. ...
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How does the collision between two atoms work?

Considering the quantum mechanical model for an atom, what exactly happens when two atoms (say, two Ca2+ ions in a Brownian motion) collide with each other? As I know, this collision is not like a ...
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Quantum mechanical photon exchange [duplicate]

Background: While trying to understand the Standard Model I stumbled on a paper that explained it in very simple terms. I recognized that I don't even understand the quantum mechanical way of the ...
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Photo pair production: differential cross section

In a scientific paper, I need for my Bachelor thesis, the differential cross section for photo pair production $\gamma\gamma\to e^{+}e^{-}$ is given as follow: $\mathrm{d}\sigma = \frac{r_{0}^{2}\...
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What does 'coupling' mean? (Laser)

I assume this question is so basic that no YT-video or paper I found answers it. But in order to understand I have to know what it refers to. I'm talking about laser coupling to be exact. I have a '...
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Pair creation and annihilation and Wheeler's one electron universe

I stumbled upon Wheeler's idea that there could be only one electron. If I understood correctly, basically the idea is that one electron moves forward and backward in time such that it appears as if ...
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Variance of an interacting quantum field in its vacuum state

A non-interacting quantum field $\hat{\phi}(x)$ can be decomposed into $a_{\textbf{k}}$ and $a_{\textbf{k}}^\dagger$. This enables us to calculate the variance of a free field. For example, the ...