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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$Z_1=Z_2$ and its relation to vertex renormalization in QED
I have been working on the full renormalization of scalar QED with self-interactions, following the steps of Schwartz’s treatment on spinor QED (Chap 19). I have 3 main questions regarding this:
Need ...
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Interferometer designed to create diffraction in free space
I designed the following interferometer:
If the light beam -theoretically- is very narrow , will light be diffracted away from point B from QED's perspective?
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Does one electron in superposition repel itself?
Consider Quantum Electrodynamics, and consider the electron field to be in a state which is a superposition of two wavepackets, each located in a different spatial position. Explicitly:
$$|\psi\rangle ...
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Elastic scattering and conservation of spin
I am trying to understand conservation of spin in QED elastic scattering in these nice notes (VJ Martin, Particle Physics, Spring 2012, University of Edinburgh): https://www2.ph.ed.ac.uk/~vjm/Lectures/...
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Scalar QED atoms - will they pass through each other?
Atoms generally do not pass through each other. This is usually attributed to the Pauli exclusion principal between the electrons (see links below).
If the electrons and nucleons were switched with ...
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Does QED explain why Moving charge produce magnetic field? [closed]
I wonder that moving charge produce magnetic fields. Now a days quantum field theory explain much of particle physics their underlying mediate particles.
But can QED explain why moving charge produce ...
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Destructive interference pattern perpendicular to photon's propagation direction
I'm studying the interference pattern for light. For example, the following is the interference pattern for double slit experiment:
I'm curious to know if there is an existing interference pattern ...
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QED: Structure of electron vertex function in the massless limit
I am working my way through Peskin & Schröder's "Introduction to QFT". In section 6.2, the formal structure of the electron vertex function $\Gamma^\mu$ is considered. From Lorentz ...
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Why is $F_1(0) = 1$? (form factor in QED)
In section 6.2 in Peskin and Schroeder (P&S) on vertex corrections, it is shown (eq 6.34) that the physical charge of the electron is given by $eF_1(0)$ (as shown by comparing the nonrelativistic ...
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What happens if obstacles (walls) been put where destructive interference occurs in double slit experiment?
If photon doesn't have probability to be in dark (destructive interference) area, what will be the effect of adding obstacles (walls) in the dark (destructive interference) area for the double slit ...
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Spinor-helicity formalism: relationship between 1 and 2 reference vector setups
The spinor-helicity formalism is usually set up so that for a massless vector boson (photon or gluon) with momentum $k$ an arbitrary reference momentum $p$ is introduced and the corresponding ...
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What is a correlation function of renormalized currents in QED?
The correlation function
$$
\langle\beta|\mathcal{T}J(x_1)\cdots J(x_n)|\alpha\rangle,\tag{1}
$$
where $J^\mu=e\bar{\psi}\gamma^\mu\psi$ is the QED current, is usually interpreted as the diagram of ...
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Can an electron be produced inside a proton?
We know that inside a proton there is a sea of quarks, antiquarks and gluons. This happens as the valence quarks emit gluons which then split into a quark-antiquark pairs. These pairs become gluons ...
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From a QED perspective, how is light created and propagated?
Using QED, what happens, exactly, when light is created?
Let's say an electron loses energy by dropping to a lower orbital, causing quantum of energy to be "emitted." What is that energy ...
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A question on IR divergence in Peskin-Schroeder chapter 6
In equation 6.64 of Peskin Schroeder, it computes $f_{\text{IR}}(q^2)$ in the limit $-q^2\to\infty$. Now, if we try to simplify the integral:
\begin{align}
f_{\text{IR}}(q^2) &=\int_0^1d\xi\;\frac{...
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Is the annihilation operator an observable (it is non-Hermitian)?
In most treatments of quantum mechanics that I have seen, observables of a quantum system are defined using Hermitian operators. The most intuitive reason for this is that Hermitian operators have ...
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In dispersive readout of a qubit coupled to a resonator, how is the measured phase shift used to determine the resonant frequency of the resonator?
In the dispersive readout of a qubit coupled to a resonator, a microwave pulse is applied to the resonator and the phase shift of the reflected pulse is used to determine the resonant frequency of the ...
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What is the observable for the optical field?
Typically, observables in quantum mechanics are associated with Hermitian operators. However, Glauber argues in 1963 ([1]) that the electric field operator $\hat{\mathbf{E}}(x,t)$ is not the relevant ...
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Are electric fields a physical input of the real world or a mathematical elaboration of Coulomb's law? If it is real what is it?
If the electric field is real, how does it affect the way we see the world? Or does nothing change? Is there a different interpretation between classical and quantum view of the electric field?
I am ...
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Some integrals in QED Renormalisation
I am currently leaning the renormalisation of QED and I have met some tricky integral that seems unsolvable. The integrals are shown in Quantum Field Theory and the Standard Model by Schwartz, page ...
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