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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In Peskin & Schroeder's QFT book page 704, the defination of electric charge is oppisite?
In Peskin book Chapter, there's QED Lagrangian in Eq.(4.3) which contains the interaction term $$\mathcal{L}_{\mathrm{int}}=-q\bar{\psi}\gamma^\mu\psi A_{\mu}\tag{4.3}.$$ From this Lagrangian we can ...
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Using Compton scattering to derive the deep inelastic cross-section for the parton model
In the second volume of The Quantum theory of Fields, Weinberg provides the inelastic cross-section for the scattering of an electron from a nucleon with four momentum $p$ based on the parton model:
$$...
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Why does an oscillating charge emulate an oscillating dipole in the far field limit?
I understand Thomson scattering as: When an EM wave is incident upon a charge causes it to oscillate in turn releasing energy as another electromagnetic wave.
In an Electrodynamics lecture we took a ...
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Classical Limit of coherent State in Jaynes Cummings Model
Im dealing with an exercise on the Jaynes Cummings model in a resonat single mode approximation. The interaction Hamiltonian in rotating wave approximation is
$$H_{int}=g\, \sigma_+\,a\,+g^*\,\sigma_-...
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What are the dimensions, width and length, of a photon?
Everyone is always talking about photon's wavelength. But what about its dimensions?
What is length and width of it?
And does it even have a point to think about such things? Or those dimensions are ...
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Scalar QED - pair annihilation into photon cross section
I just spent the last three days trying to compute the cross section of a process of pair annihilation of complex scalars to a pair of photon in scalar QED.
For some reason I don't seem to be able to ...
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Electron Muon Scattering
I have been doing studying in advance for Dirac Equation and stumbled upon the math on calculating the spin-averaged amplitude $\bar{M}^{2}$ for the electron muon scattering process. Below is an ...
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Is the electric force really proportional to the charge it acts on? [closed]
Of course we all know Coulomb's law, which includes the fact that the electric force experienced by an object is proportional to its charge. My question is: Does this hold to the best of our current ...
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Casimir effect and lambshift, uncontroversial evidence of the zero point field? (SED)
"By far the most accepted evidence of the reality of the zpf is the Casimir effect, that is, the force between two parallel neutral metallic plates resulting from the modification of the field by ...
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Coupling Constant, $r^{-2}$ vs $r^{-1}$ behaviour
I'm reading this Wikipedia article and I find some details quite particular and useful to have another look on the topic:
https://en.m.wikipedia.org/wiki/Coupling_constant
I have a doubt about the ...
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What sort of QED-like theories can have non-quantized charge?
It is often said that the existence of a single monopole would force electric charge to be quantized, due to Dirac's argument. However, one can write down theories like QED that, independently of the ...
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Topological current in (2+1)D spinorial electrodynamics
Giving the coupled Dirac equations for $\psi$ and its conjugate $\bar{\psi}$ in 2+1:
\begin{align}
(i\gamma^\mu\partial_\mu-m)\psi&=qA_\mu\gamma^\mu\psi,\\
\bar{\psi}(i\gamma^\mu\partial_\mu+m)&...
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Is QED asymptotically free in lower dimensions?
It is well-known that QED (=quantum electrodynamics) is NOT asymptotically free in spacetime dimension $4$.
However, I wonder if it becomes asymptotically free in lower dimensions, such as $2+1$ ...
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Localized wavefunction and double slit experiment
I am trying to have better understanding of localized wave functions. Apparently free particle de Broglie waves are NOT normalizable and act as delocalized functions which was the original rationale ...
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Vacuum polarization
Interaction vertex of QED are like:
\begin{equation}
e \bar{\psi} {A\mkern-9mu/} \psi
\end{equation}
But we can't write a vertex where a particle-antiparticle pair annihilates in just 1 photon, due to ...
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Does the wave function of localized s-orbitals radius reduce under extreme solid-state pressures prior to degeneracy?
Under extreme conditions not found in nature, say low temperature solids that are under extreme pressures* prior to collapse into degenerate matter states, does a localized s-orbital radius reduce ...
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Which theory/model explains electrons movement inside a transmitting antenna? [closed]
I have an understanding of electrical circuits, however I am very interested to know more about electromagnetic waves radiation.
In particular I want to know how an oscillating voltage causes the ...
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How to expand Electromagnetic fields in term of Laguerre–Gaussian (LG) beams?
I was studying canonical quantization for the electromagnetic fields. I know that we can expand our fields in other normal modes which one of them is the Laguerre–Gaussian (LG) wave set but in most ...
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One-loop potential correction in QED (Lamb shift)
Vacuum polarization 1-loop in QED gives another term in potential, named Lamb shift. Potential in terms of momentum $p^2$ is:
$$V(p^2)= \frac{e^4_R}{2\pi^2p^2} \int_0^1 x(1-x)\ln[1-\frac{p^2}{m^2}x(1-...
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Quantization of a doughnut field
I am trying to understand quantization. There is a big theory in books of QFT, but none of them is telling explicitly what to do in not trivial cases. At least I haven't understood it yet.
I know that ...
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Derivation for Quantum optics dipole radiation formula
An often used formula for the radiation field of a dipole is the following one:
\begin{align}
\vec{E}(t, \vec{x}) = \frac{1}{4 \pi x^3} ( 3 \hat{x} [ \hat{x} \vec{d}(t_r)] - \vec{d}(t_r) ) + \frac{1}{...
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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 ...
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Possible mistake in Lancaster’s QFT pg 351?
In QFT for the gifted amateur by Lancaster pg 350, the matrix element for bhabha scattering is calculated. The spinor for an incoming electron is shown as $u(p) = (0,0,1,0)$ but on the next page when ...
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Evaluation of functional derivative of effective action
I'm trying to understand a calculation in appendix A of this paper https://arxiv.org/abs/2204.04197, however I don't understand how they end up with equation (125) and I think I am going wrong in the ...
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Quantization of radiation with canonical conjugate variables
I am reading the Introduction to quantum optics book and I am a bit stuck at the quantization of electromagnetic field (around page 317).
The problem in this case is that we can't just express the ...
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Understanding the factorization of subleading soft contributions-massless QED
I am reading The SAGEX Review on Scattering Amplitudes Chapter 11: Soft Theorems and Celestial Amplitudes. In subsection 2.2, the subleading soft photon theorem is derived. The result is
$$A^{\mu}=\...
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What causes the direction of a photon?
I understand my question sounds stupid but hear me out. I wondered if protons or any charged particle could generate photons and I found this wonderful answer that says yes: Does shaking an atom ...
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Limitations of describing QED interactions in the Coulomb gauge?
When we work with the S-matrix operator to describe interactions between the quantized Maxwell field and a classical source or a Dirac field, are there any limitations one needs to keep in mind when ...
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Broken symmetry and three-photon vertex
I know that loop-level three-photon vertex in QED is zero since the contribution from fermion and antifermion cancel each other.
Also, from what I know this has something to do with gauge invariance ...
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Does the $\frac{4}{3}$ problem of classical electromagnetism remain in quantum mechanics?
In Volume II Chapter $28$ of the Feymann Lectures on Physics, Feynman discusses the infamous $\frac43$ problem of classical electromagnetism. Suppose you have a charged particle of radius $a$ and ...
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Fermion Propagator in Positron-Photon (Compton) Scattering
I’m calculating some Feynmann Amplitudes, in particular the Positron-Photon (Compton) Scattering.
In general the fermion propagator is:
$$iS_F(q) = \frac{i(\gamma^{\mu}q_{\mu}+m)}{q^2-m^2}$$
The ...
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Do attosecond lasers allow us to further constrain the location of electrons within the established probability clouds, via time?
It has only been within the last few years that I learned the atomic model I grew up with (the Bohr model) was wrong, and that I should instead be thinking about electron orbitals as a cloud of ...
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The enigma of photon behavior, photon spatial co-inhabitance
The notion that multiple photons can occupy the same spatial coordinates seems perplexing. How is this experimentally validated, considering the intricate challenges and oddities it presents?
Imagine ...
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Physical states in Gupta-Bleuler quantization
I'm reading Timo Weigand notes for Gupta-Bleuler quantization of free EM field.
On page 109, Author has made the following statements.
The Gupta-Bleuler condition for physical state is
$$|\vec{p},\...
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Spherical Electromagnetic Radiation Propagating Inwards
Suppose I produce a large number of photons subject to the following conditions:
The photons are produced at (approximately) the same time at (approximately) the surface of a sphere (if I'm not ...
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Total Angular Momentum operator in spinor-helicity formalism
I am reading Evidence for a new Soft Graviton theorem, by Cachazo and Strominger. At some point, they express the relation
$$J_{\mu\nu}\sigma^{\mu}_{\alpha\dot{\alpha}}\sigma^{\mu}_{\beta\dot{\beta}}
=...
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How to prove $-i\gamma_2u_{s}^*(p)=v_{s}(p)$ for Dirac spinors?
It should be true and it's obvious for $p^{\mu}=(m,0,0,0)$, but I'm having trouble with the gamma matrices Algebra and prove it for general momentum.
I'm using Weyl representation:
$$u_{\uparrow}=\...
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What is the full QED Lagrangian with physics units written out?
I wonder what the QED Lagrangian would look like if you carefully write out all units of the terms and make sure they are consistent. I think there is something missing about Coulomb.
Can you write ...
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Planck-Einstein energy equation for a spin-2 particle?
The $$E=hf$$ Planck-Einstein energy equation applies strictly only for SU(2) elementary single particles like the photon. Even when calculating with this equation the rest energy of an electron we ...
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A problematic equation for Dirac field:$[\psi,\hat{J_z}]=J_z\psi+i(x{\partial \psi\over\partial y}-y{\partial\psi\over\partial x})$ How is this true?
The Dirac field is quantized as:
$$\psi(x^\mu)=\int{d^3 p\over(2\pi)^3\sqrt{2\omega_p}}[a_s(p)u_s(p)e^{-ipx}+b_s^{\dagger}(p)v_s(p)e^{ipx}]$$
In the title:$$[\psi,\hat{J_z}]=J_z\psi+i(x{\partial \psi\...
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Question on Spinor choice in QED
In QED (see Peskin and Schoeder's book on QFT or Srednicki's book), to determine the fermion wave-function, we usually start with a spinor of a massive particle that is not moving, say
$$u_+(\vec{p}=\...
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Under what conditions does a beam splitter entangle two input photons?
There is a dispute on PhysicsForums related to what are the conditions necessary for two photons to be entangled by a beam splitter. Lots of references given by the forum users but they never arrive ...
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Quantization of electrodynamics in a nonlinear dielectric medium
Recently I read this paper https://doi.org/10.1103/PhysRevA.30.1860 by Hillery and Mlodinow about the (canonical) quantization of electrodynamics in nonlinear dielectric media. They assume that the ...
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Ward-Takahashi Identity in QED
P&S write in Section 7.4 on page 238:
We will prove the Ward-Takahashi identity order by order in $\alpha$……The identity is generally not true for individual Feynman diagrams; we must sum over ...
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Which spinor should be used for an outgoing proton if we treated it like a point particle? $\bar{u}(p)$ (as for electron) or $v(p)$ (as for positron)
Consider the Rutherford scattering $e^-p^+ \rightarrow e^-p^+$
If a proton is a treated as a heavier positron:
$i\mathcal{M}=(-ie)\bar{u}(p_3)\gamma^{\mu}u(p_1)i\Pi_{\mu\nu}(-ie)\bar{v}(p_2)\gamma^{\...
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Semi-classical derivation of maximal magnetic field in the Universe
I'm looking for all (or most) theoretical semi-classical derivations of the maximal magnetic field intensity that there may be in the Universe. As an example, this paper evaluate a maximal field of ...
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Is there a way to visualise / understand intuitively the curvature in the $U(1)$ circle bundle responsible for the electromagnetic force?
In general relativity we have embedding diagrams of different slices of spacetimes. These can be quite helpful to understand the geometry of a given pseudo-Riemannian manifold (especially when the ...
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How can we prove that Compton scattering has two equivalent terms in the $S$-matrix expansion?
Consider the Compton scattering
$$e^{-}(p,s)+\gamma(k,\lambda)\rightarrow \gamma(k',\lambda')+e^{-}(p',s')$$
To calculate the process' amplitude one has to compute the matrix element
$$S_{fi}=<f|\...
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How to recognize Feynman diagrams from the $S$-matrix expansion?
I'm studying scattering processes in QED and one usually have to compute first of all the Scattering matrix
$$\hat{S}=T\biggl (\exp\{-i\int d^{4}x:\bar{\psi}(x)\gamma_{\mu}\hat{A}^{\mu}(x)\hat{\psi}(x)...
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Fermion Propagator
Will the fermion propagator change if instead of deriving it from the Lagrangian
$$\mathcal{L}=i\bar{\Psi}\gamma^{\mu}\partial_{\mu}\Psi
-m\bar{\Psi}\Psi\tag{1}$$
I derive it from
$$\mathcal{L}'=\frac{...
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