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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858 views

Did the Feynman heuristic of “simple effects have simple causes” fail for spin statistics?

Someone here recently noted that "The spin-statistics thing isn't a problem, it is a theorem (a demonstrably valid proposition), and it shouldn't be addressed, it should be understood and celebrated." ...
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703 views

Classical electrodynamics as an $\mathrm{U}(1)$ gauge theory

Preface: I haven't studied QED or any other QFT formally, only by occasionally flipping through books, and having a working knowledge of the mathematics of gauge theories (principal bundles, etc.). ...
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441 views

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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1answer
807 views

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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1k views

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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239 views

Path Integral on Feynman Hibbs: Interaction of EM field and matter, how can we get to equation (9.68) from (9.67)?

On Feynman Hibbs "Quantum Mechanics and Path Integrals", the equation (9.67) describe the transition amplitude of the matter (for example an atom) to go from the state $M$ to the state $M$ when it ...
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297 views

In QED/Yang Mills, why do fermions contribute 4 times as much as scalars to vacuum polarization?

Consider a Yang-Mills theory in $4D$ over a gauge group $G$ $$ \mathcal{L} = - \frac{1}{4} F^{a\mu\nu}F_{\mu\nu}^a + \bar \psi i D_\mu \gamma^\mu \psi + (D_\mu \phi)^\dagger D^\mu \phi $$ where $\...
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318 views

What is the effective (quantum) lagrangian of a fermion field for fixed electromagnetic field?

... or, put it another way, what are the loop corrections to the dirac equation in the presence of a fixed (external) electromagnetic field?. Background Let $\mathcal L=\frac{1}{2}(\partial\phi^2+m^...
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131 views

Measuring the Dirac field

If the Dirac field $\psi(x)$ is to the electron as the Electromagnetic field is to the photon, why is it that we can measure the Electromagnetic field, whereas the Dirac field we cannot?
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238 views

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 "...
6
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141 views

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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120 views

Photons and Electric Current

I am trying to understand how photons as the force carrier for the electromagnetic force (or field) manifest themselves in a flow of electric charge, i.e. an electric current. Both standard (...
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103 views

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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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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174 views

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). ...
5
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1answer
88 views

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 ...
5
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2answers
191 views

When will a quantum measurement occur?

I am confused about the nature of quantum measurements. In short: if a particle is coupled with a field, when will the wave collapse. A field might be coupled to a particle for a long time, and ...
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1answer
92 views

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 ...
4
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1answer
55 views

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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45 views

Do longitudinal and scalar have anything to do with Faddeev-Popov ghosts?

In his this book, Hatfield calls ghosts the negative states appearing in the covariant (Gupta-Bleuler) quantization prescription of the electromagnetic field (page 89). When discussing Yang-Mills ...
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111 views

What is the problem of non-pertubative quantisation?

In reading books about quantisation, there is (sometimes hidden) the claim, that quantisation is done using a pertubative approach. You look at the free field, find that it is essentially a sum of ...
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148 views

Scattering, absorption, emission and virtual photons

From reading many questions on this site I have the following conclusions: Interaction of a photon and a free electron is an instantaneous process of scattering (transfer of momentum) between said ...
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158 views

EM Field Quantization in Spherical polars

Is it possible to quantize the electromagnetic field in spherical polar coordinates instead of cartesian ones? Such that creation and annihilation operators correspond to harmonic oscillator modes ...
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401 views

Gauge invariance and the unitarity

I want to discuss the relation between the unitarity and the gauge invariance. Suppose we have for simplicity an abelian gauge theory (say, EM theory). We want to quantize it in terms of 4-potential $...
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109 views

On why in transparent media light speed is altered by elastic scattering of photons and their path lengths

I have read this: https://en.wikipedia.org/wiki/Higgs_boson Where it says: "Symmetry breaking in optics In a vacuum, the light of all colours (or photons of all wavelengths) travels at the ...
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157 views

How does one extract classical results from QED Lagrangian?

A well known result from classical electrodynamics for the total energy density of a charged spherical shell is, $$ u = \frac{3e^2}{32 \pi^2 \varepsilon_0 r^4}, $$ How would you extract that result ...
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167 views

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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448 views

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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449 views

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 photon-...
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193 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 ...
4
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1answer
111 views

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 ...
4
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1answer
386 views

Divergent self-energy of point charges in Classical Electrodynamics

Assuming the electron to be a classical point particle, if one calculates the self-energy one finds $$U=-\frac{e^2}{8\pi\epsilon_0r}$$ which diverges as $r\rightarrow 0$. Therefore, the measured mass ...
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27 views

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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51 views

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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2answers
81 views

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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51 views

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 ...
3
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1answer
61 views

Electromagnetic current operator using Feynman rules

In the calculus of the electron anomalous magnetic moment some text books usually calculates the forms factors from $\Gamma_{\mu}$ in the expression bellow $\left<p',s'|J^{em}|p,s\right> = \...
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60 views

Electron interaction term in a external field

In quantum electrodynamics an electron $e_0$ interaction with an external field is given by term $\mathcal{L}_{\text{int}}\sim \bar{\psi}\gamma^\mu A_{\mu}^{c}\psi$ Where $A_{\mu}^{c}$ is ...
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If I move one electron does the rest of the Universe react to that change from QFT perspective?

I apologize if this is something super trivial: I couldn't find any answers myself so decided to finally ask my first question on Physics.SE. Classically speaking, if I move one electron from A to B (...
3
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1answer
90 views

Non-linearities in Lagrangian of a scalar field coupled to point-like source

I have an exercise where I did not manage to understand the questions. Basically, I have this Lagrangian \begin{equation} \mathcal{L}=\frac{1}{2}(\partial \pi)^2-\frac{1}{\Lambda^3}(\partial \pi)^2\...
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Identifying diagrams for optical processes

I was reading some papers on the study of the optical properties of some metals and came upon these conference proceedings by Hopfield from 1972. They are on the study of the infrared properties of ...
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Is the physical mass of the electron a gauge invariant quantity?

In Lattice, one cannot calculate gauge non-invariant quantities, such as the quark mass. This is because one averages over the gauge and gets 0. One way to get around the issue is to fix the gauge. ...
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513 views

Proof non-convergence of perturbation in QED

This is an attempt to ask separately about aspects of my previous question, which was closed as too broad. Note that I strongly prefer results that are or can be made mathematically completely ...
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108 views

What is the evidence of the field-particle relation?

In the traditional textbook approach to QFT, the Fock space is presented with not much motivation and in all books I've seem nothing is said about the fact that in QFT there are uncountably many ...
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52 views

What are the mechanisms that cause the vacuum to be nonlinear to EM excitation?

Consider a electromagnetic excitation that is confined in time, and locally looks like a plane-wave traveling in a vacuum: $$ \mathbf{E}(\mathbf{r},t) = \mathbf{\hat{x}}E_0 \cos(\mathbf{k}\cdot\...
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Do photons and matter wavefunctions both reflect off of mirrors the same way?

Does a photon reflect off a mirror in the same way a bosonic wavefunction does? If they are different, what are the physical mechanisms that cause those differences? Additionally is this the same for ...
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How do I show that there is no supersymmetry breaking in two-dimensional $U(1)$ gauge theory

My question is regarding supersymmetric $U(1)$ gauge theory in two dimensions. In particular, I am interested in the supersymmetry which is preserved by Witten's topological A-twisting. It seems to me ...
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504 views

Richard Feynman - QED: The Strange Theory of Matter and Light

After reading the book QED: The Strange Theory of Light and Matter, an adaptation of four lectures Richard Feynman gave at the University of Auckland, I gained a greater understanding of QED. I am not ...
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61 views

Effective field theory with coordinate dependent “axion”

Suppose the theory of fermions interacting with EM field and the axial 4-vector $b_{\mu}$: $$ S = \int d^{4}x \bar{\psi}\gamma^{\mu}(i\partial_{\mu} + eA_{\mu} +\gamma_{5}b_{\mu})\psi $$ We want to ...
3
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191 views

Could sonoluminescence be the result of the Casimir Effect?

My question concerns Sonoluminescence. I was amazed to learn that collapsing cavitations in liquids generate temperatures greater than 20,000 Kelvin. Is it possible that the vast amount of energy ...