# 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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### 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 ...
1 vote
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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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### 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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### 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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### 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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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 ...