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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Questions about QED Corrections to Coulomb's law and Electromagnetic Wave Equation
As a disclaimer, this is somewhat similar to this unanswered question, but not entirely.
In standard QED theory, it is frequently demonstrated that the derivation of the Coulomb Potential can be found ...
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Photon Mass Regulator in IR divergences
On Schwartz's QFT page 333, he metions that there is infrared divergence when we try to renormalized the two-point function of electron field in on-shell substraction scheme,
$$\frac{d}{d\,p_{\mu}\...
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Parametric down-conversion - QFT necessary?
In quantum optics, one ususally starts by quantizing the free electric field and obtains an expression for the electric field operators:
$$ E(\vec{r},t) = \sum_{\vec{k},p} C_{\vec{k}} \vec{e}_{\vec{k},...
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QED with massless fermions
Consider QED such that physical mass of fermions vanishes. Is it true that their bare mass also vanishes?
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Link between photon helicity and polarization of $A^\mu$ electromagnetic potential
From Wigner theorem we know that the irreducible unitary representation of the Poincarè group for massless and spin 1 particle is labelled by the momentum $p_\mu$ and the two possible helicity $+1,-1$ ...
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Photon propagator in path integral vs. operator formalism
I am self-studying the book "Quantum field theory and the standard model" by Schwartz, and I am really confused about the derivation of the Photon propagator on page 128-129.
He starts ...
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Calculating a Feynman diagram with the helicity basis
In the book by Peskin and Schroeder, they calculate the leading order diagram for the process $e^- e^+ \to \mu^- \mu^+$ (see page 136 for the labelling of the momenta). They do this in two ways: using ...
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Independence of $S$-matrix of $\xi$-gauge in QED
On page 298 in Peskin and Schroeder, the authors attempt to argue that the $S$-matrix should be independent of the $\xi$-gauge in QED. However, I don't understand their argument, in particular the ...
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$ \pi^0\to \gamma\gamma$ parity conservation
Let's consider the decay process $\pi^0\to \gamma \gamma$. After we spontaneously broke the chiral symmetry of QCD coupled to an abelian gauge field $A^\mu$, we end up with the Goldstone boson ...
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Some calculation in Schwartz's Quantum field theory eq. (16.39)
In Schwartz's Quantum field theory and the standard model, p.307 he derives a formula:
$$ \Pi_2^{\mu \nu} = \frac{-2 e^2}{(4 \pi )^{d/2}}(p^2g^{\mu\nu}-p^{\mu}p^{\nu})\Gamma(2- \frac{d}{2}) \mu^{4-d} \...
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Weisskopf and self-energy
I am working my way through the 1934 paper by Weisskopf on the self-energy of the electron and is much helped by the English translation found here. I do have some difficulties with section 2 of this ...
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Is it possible to lower the energy of the vacuum?
The energy of the vacuum is given by $$\sum_k \frac{1}{2}\hbar\omega_k.$$ However the frequency $\omega_k$ depends on the wavevector $k$ and some constants like the speed of light $c$, which in turn ...
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What is the energy of a photon in an electron-muon scattering?
Currently I am reading about this process in an Introduction to Quantum Field Theory by Peskin and Schroeder (pages 153-154). It should be mentioned that they are working in a center-of-mass (CM) ...
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Unitary Gauge Removing Goldstone Bosons
The Lagrangian in a spontaneously broken gauge theory at low energies looks like
$$ \frac{1}{2} m^2 ( \partial_\mu \theta - A_\mu )^2 $$
and the gauge transformations look like $\theta \rightarrow \...
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How is light interference explained with photons?
In the classical model of light as an EM wave, interference is a trivial consequence of the linearity of the wave equation. Now, if we model light as collections of photons, how is light interference ...
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Feynman rule for scalar QED vertex
A popular problem in QFT textbooks and courses is to derive the Feynman rules for scalar QED. Usually, this theory is presented via the following Lagrangian density:
$$\mathcal{L} = (D_\mu\phi)^\...
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Particle and momentum Flow for complex scalar or fermion field
When i look at complex scalar fields or fermion fields, i have my $\psi^\dagger$ as my anti particle and $\psi$ as my particle, same for $\phi^\dagger$ and $\phi$. When i now draw the Feynman diagrams ...
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Does the creation operators for photons with different polarization commute?
Let $\hat{a}^{\dagger}_{\sigma}$ be the creation operator of a photon with the polarization $\sigma $ towards some reference. What are the commutator relations for the creation operators of a photon ...
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How are quantum states of particles represented in particle processes?
For example, lets say we have an electron-positron annihilation scenario. What will be the density matrix representing the quantum state of the electron and the positron? What will be the density ...
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Field strength renormalization for fermions
Following section 7.1 and 7.2 in Peskin and Schroeder (P&S), I've tried to consider what the derivation of the LSZ formula looks like for (spin $1/2$) fermions (in the text, they explicitly ...
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Is there a second-order non-linear addition to Maxwell's equations?
Maxwell's equations are famously linear and are the classical limit of QED. The thing is QED even without charged particles is pretty non-linear with photon-photon interaction terms. Can these photon-...
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Literature on intense field QED
Does anyone happen to know a good book or notes on intense field QED, for example about Volkov states and the Furry picture? To give you an idea of my pre-knowledge: I am a physics graduate student ...
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Feynman diagrams in Yukawa interaction
I want to understand drawing Feynman Diagrams better, therefore I wanted to draw some for the Lagrangian with a Yukawa interaction term:
$$L = \bar{\psi}(i \partial\!\!\!/ - m)\psi - g \bar{\psi}\phi \...
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Independence of $S$-matrix in QED of a gauge of EM field
Due to existence of several ways to fix a gauge of an EM field in QED, there are several ways to quantize it. That leads to non-uniqueness of photon propagator and hence to non-uniqueness of integrals ...
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Why is finding a mathematical basis for the fine-structure constant meaningful?
I was reading QED by Richard Feynman and at the end he mentions that:
There is a most profound and beautiful question associated with the observed coupling constant, $e$ – the amplitude for a real ...
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Charge Renormalization in Abelian Gauge Theory under General Gauge Fixing Conditions
In scalar QED or fermionic QED, the relationship between bare quantities (subscript "B") and renormalized quantities is given by
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
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Radiation reaction in the ground state of an atom [duplicate]
In a typical bound energy eigenstate of an atom the magnitude of the wave function is time independent only phase changes in time. So I expect no radiation reaction force in the ground state. However ...
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Long-range approximations of the Uehling interaction
A common approximation to the
\begin{equation}
U(\vec{r})=-m\frac{\alpha(Z\alpha)}{\pi}
\int_1^\infty\mathrm{d}u\frac{\sqrt{u^2-1}\left(2u^2+1\right)}{3u^4}\frac{\exp(-2mur)}{mr}
\tag{$\star$}
\end{...
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QED without fermions? [duplicate]
Is it possible to write down a sensible analog to QED but without fermions? Or better yet, with only scalar particles? Would two scalar fields with an interaction term $\lambda \phi_1 \phi_2^2$ lead ...
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How is partial reflection of light by two surfaces explained?
I am reading QED by Richard Feynman and he explains how changing the thickness of glass results in a change in the probability of photons reflecting off the glass back to the photomultiplier.
However, ...
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