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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Different statements of the Heisenberg uncertainty principle

I know that from the Heisenberg uncertainty principle, ∆x∆p=ℏ/2 . And I know that this equation can be rewritten as ∆t∆E=ℏ/2. From QED I also know that the equation ∆t∆E=ℏ/2 claims that some energy ...
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How to “transfer” indices from dot product to metric?

In this source, the author (Andrzej Pokraka, Solutions to problems from Peskin & Schroeder) is computing an integral related to scalar QED. In the step where the equation is labelled (29), the ...
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What does matter look like in the absence of photons?

Another question inspired by this one on alternative standard models. Greg Egan's story Wang's Carpets (or the similar segment of the larger novel Diaspora) sketchily describes a universe with no ...
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Evaluation of Wilson loop in QED

I'am trying to figure out the evaluation of the expectation value of the Wilson loop for QED. (Its actually the problem 15.3 in Peskin and Shroeder) Lets say the Wilson loop is $W(x) = exp(-ie\oint_P ...
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Can we remove IR divergences in continuous QFT?

During a QFT class, my professor briefly explored the fact that infrared (IR) divergences can be removed from QED by considering "soft" photons that have an energy inferior to the detector sensitivity,...
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What is the real problem in the free body problem?

Ions are produced when an EM neutral atom gains EM charge by gaining or losing electrons, by collision with other charged particles or photons. The study of such collisions is of fundamental ...
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144 views

Difference between Coulomb law and QED

According to Coulomb law, the electromagnetic force between point charges separated at zero distance is infinite. Does QED explains the same result, or there is any difference?
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68 views

Why is the spontaneous emission a big deal?

In spontaneous emission, an electron in an energetically higher state jumps to an energetically lower state. This seems a simple phenomenon. Why is it called a quantum mechanical effect? What was so ...
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133 views

Existence of Photon

I was reading Feynman lectures on physics (volume 1) when I encountered the following paragraph: Returning again to quantum mechanics and fundamental physics, we cannot go into details of the ...
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Confused about the anapole (toroidal) moment

I am a bit confused about the existence of the anapole moment. As far as I understand, in order to fully describe a charge-current distribution, one needs, beside the normal electric and magnetic ...
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108 views

Importance of $\alpha/\pi$

What is the physical meaning or importance of $\alpha / \pi$ ($\alpha$ being the fine-structure constant)? I have seen that it is the parameter in the expansion of the g-factor but I can not reach to ...
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What is the resulting state from these field operators operating on this photon state?

$\newcommand{\ket}[1]{\left|#1\right>}$ I'm doing research into spontaneous parametric down conversion for an assessment. I have derived the hamiltonian and, from here used perturbation theory to ...
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What exactly does it mean to say that QED is of “universal strength and form”?

In a paper from 1961 (Gauge Theories of Vector Particles, Glashow and Gell-Mann), the authors describe quantum electrodynamics thusly: "It is of universal strength and form..." What exactly does ...
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Do electrons really perform instantaneous quantum leaps?

This is not a duplicate, non of the answers gives a clear answer and most of the answers contradict. There are so many questions about this and so many answers, but none of them says clearly if the ...
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102 views

What is the intuitive reason why matter and antimatter should be highly reactive?

Common knowledge has it that when an amount of matter and an amount of antimatter come anywhere near each other, they annihilate, leaving nothing but "pure energy". In more technical terms, maybe we ...
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Peskin and Schroeder Section 7.1 Mass Shift

I'm slowly reading my way through Peskin and Schroeder. Near the end of section 7.1 they compare the mass shift of the electron from QFT to the classical value, both of which are divergent but in ...
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Real space description/information of photons

recently I read a paper about some special tratment in QED (https://doi.org/10.1103/PhysRevLett.122.193603) and they used a lot the term "real space description" or "real space information" of photons....
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What are zero-energy Rindler photons?

In the discussion of the Unruh effect and Bremsstrahlung (e.g. here) I always come across "zero-energy Rindler photons". What exactly are these? Shouldn't a zero-energy photon correspond to a static ...
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Commutation relations in Gupta-Bleuler quantization

Quantization of the free electro-magnetic field has essential differences in comparison to quantization of say scalar or massive vector fields. In fact there are different approches to it. One of ...
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Reflectance and transmittance equations for metal thin film

The Fresnel's equations no long work when the thickness of the metal thin film is thinner than skin depth. For example, the reflectance of a metal thin film is always the same according to fresnel's ...
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Vector current conservation in vertex correction

Recently, I was calculating this observable: $\langle p s|\bar\psi(0)\gamma^{\mu}\psi(0)|ps\rangle$ Where we only consider the QED case. $\psi$ corresponds to massless Dirac fermion field, p is the ...
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Scalar electrodynamics “seagull” vertex factor

By expanding the covariant derivative of the Scalar QED lagrangian one gets the following term, sometimes called "seagull" vertex. $$\mathcal{L}_{seagull} = -q^2A_\mu A ^\mu \phi^\dagger \phi$$ Most ...
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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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193 views

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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50 views

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 ...