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 definition of electric charge is opposite?
In Peskin's book Chapter 4, the 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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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
$$u_+(\vec{p}=\...
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A problematic equation for Dirac field:$[\psi,\hat{J_z}]=J_z\psi+i(x{\partial \psi\over\partial y}-y{\partial\psi\over\partial x})$ How is this true?
The Dirac field is quantized as:
$$\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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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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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:
$$u_{\uparrow}=\...
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Total Angular Momentum operator in spinor-helicity formalism
I am reading Evidence for a new Soft Graviton theorem, by Cachazo and Strominger. At some point, they express the relation
$$J_{\mu\nu}\sigma^{\mu}_{\alpha\dot{\alpha}}\sigma^{\mu}_{\beta\dot{\beta}}
=...
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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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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
$$|\vec{p},\...
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Which spinor should be used for an outgoing proton if we treated it like a point particle? $\bar{u}(p)$ (as for electron) or $v(p)$ (as for positron)
Consider the Rutherford scattering $e^-p^+ \rightarrow e^-p^+$
If a proton is a treated as a heavier positron:
$i\mathcal{M}=(-ie)\bar{u}(p_3)\gamma^{\mu}u(p_1)i\Pi_{\mu\nu}(-ie)\bar{v}(p_2)\gamma^{\...
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Is there a way to visualise / understand intuitively the curvature in the $U(1)$ circle bundle responsible for the electromagnetic force?
In general relativity we have embedding diagrams of different slices of spacetimes. These can be quite helpful to understand the geometry of a given pseudo-Riemannian manifold (especially when the ...
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How to recognize Feynman diagrams from the $S$-matrix expansion?
I'm studying scattering processes in QED and one usually have to compute first of all the Scattering matrix
$$\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
$$\mathcal{L}'=\frac{...
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Gauge invariance in QED with just fermion transformations
I've got myself confused about a basic question. If we have a gauge-invariant operator $\mathcal{O}$ whose expectation value is
\begin{equation}
\left\langle\mathcal{O}\left(x_1, \ldots, x_n\right)\...
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How does QED describe the electromagnetic scattering between two neutral fermions?
Fermions with no electric charge may carry magnetic moments e.g., the neutron. Since particles with magnetic magnetic moments interact, they're expected to scatter off each other electromagnetically. ...
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Is there an intuitive way to understand the Lagrangian for magnetic and electric dipole moment?
From the textbook I learned that the electric dipole moment (EDM) and magnetic dipole moment (MDM) has the following Lagrangian:
$$\mathcal{L}_{EDM}=F_{\nu\mu}\bar{\psi}\gamma^{5}\left[ \gamma^{\nu},\...
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Quantifying the quantum electric field for $E$-fields that are not waves
In every physicists training, an electrostatics course will show how to solve Maxwell's equations for different systems, solving for the $E$-field at different points in space.
A separate solution to ...
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Meaning of a Feynman diagram in proof of Ward-Takahashi identity in chapter 7 of Peskin and Schroeder
I'm trying to understand what the external photon in this diagram (page 238 in P&S) corresponds to exactly. This diagram is supposed to be a contribution to the Fourier transform of a QED ...
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Can a consistent theory of electric force exist where charges of equal sign attract each other and charges of opposite sign repel each other?
I am preparing tomorrows lesson about electrostatics and the Coulomb law and wondered the following:
By simple experiments we can show that the electric force can be attractive and repulsive, so we ...
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Basis vectors for quantum electrodynamics
The following unnormalized vectors are solutions to the Dirac equation.
\begin{align*}
u_1&=\begin{pmatrix}E+m\\0\\p_z\\p_x+ip_y\end{pmatrix}
\exp\left(\frac{i\phi}{\hbar}\right)
%
& v_1&=\...
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Why isn’t electric potential energy involved in the calculation of pair production?
When I learned about energy conservation in pair production, we only considered the energy of matter and light. Why isn’t the electric potential involved? Also why isn’t the gravitational potential ...
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Massless QED modified Lagrangian
Consider a massless theory of QED, with Lagrangian
$$\mathcal{L}_{QED}=
-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\bar{\Psi}i\gamma^{\mu}\partial_{\mu}\Psi+
e\bar{\Psi}\gamma^{\mu}A_{\mu}\Psi$$
Is there any ...
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Scalar particle Compton scattering using relativistic Lagrangian formulation of electromagnetism
We know that parallel to scalar QED, a common formalism that describes a massive particle coupled to electromagnetism is through a relativistic worldline formalism, which writes
$$\mathcal{S}=\int\ ds\...
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Does the electric charge run differently with energy for electrons and for W bosons?
Do the running with energy of the electron charge and of the W boson electric charge differ or are they the same?
Is there any theoretical or experimental evidence that allows the comparison?
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Feynman rules for scalar QED [closed]
Can i have a derivation for the Feynman rules of scalar QED?
I don't understand the ones i find online such as the one in the link https://canvas.harvard.edu/files/936391/download?download_frd=1&...
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Finding momentum of an electron using quantum mechanics in Fermi's 1932 paper
I was reading Fermi's 1932 paper "Quantum Theory of Radiation". I was able to understand the paper until this particular derivation (which was excluded).
$u_m,u_n$ are the eigen-functions ...
