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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Radiative corrections to Coulomb’s law and Euler-Heisenberg theory
Maxwell's electrodynamics is the classical limit of QED (quantum electrodynamics). Using Maxwell's equations, the electrostatic (Coulomb) potential of a point charge is obtained as $\Phi \propto \frac{...
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Deriving non-relativistic potentials from QFT
Some systems, like atoms, are described well by quantum mechanics, where one just gives the Hamiltonian in the form $H=T+V$ and computes the eigenvalues and eigenvectors of this operator to figure out ...
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gauge invariance of the Feynman amplitudes
When we calculate the photon polarization sums over amplitudes,
$$X=\sum\limits_{r=1}^{2}|\mathcal M_r|^2=\mathcal M_\alpha\mathcal M_\beta^*\sum\limits_{r=1}^{2}\epsilon_r^\alpha\epsilon_r^\beta$$
...
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Why does the Dirac equation work for the hydrogen atom?
The Dirac equation works well for predicting the spectrum of the hydrogen atom, famously incorporating relativistic effects like fine structure. Yet, there seems to be a sense in which this is ...
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Path Integral on Feynman Hibbs: Interaction of EM field and matter, how can we get to equation (9.68) from (9.67)?
On Feynman Hibbs "Quantum Mechanics and Path Integrals", the equation (9.67) describes the transition amplitude of the matter (for example an atom) to go from the state $M$ to the state $M$ ...
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Integration & bremsstrahlung calculation
In this paper (relevant pdf section) that I'm reading, involving the calculation of bremsstrahlung in electron proton scattering (diagram below), the author calculates the integral over outgoing ...
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Do EM waves transmit spin polarization?
Suppose you have a normal dipole antennae (transmitter and receiver) . Spin polarized current (as opposed to normal current) is sent into the transmitter, it emits an EM wave and the Receiver receives ...
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In QED/Yang Mills, why do fermions contribute 4 times as much as scalars to vacuum polarization?
Consider a Yang-Mills theory in $4D$ over a gauge group $G$
$$
\mathcal{L} = - \frac{1}{4} F^{a\mu\nu}F_{\mu\nu}^a + \bar \psi i D_\mu \gamma^\mu \psi + (D_\mu \phi)^\dagger D^\mu \phi
$$
where $\...
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How can QED by predictive if it diverges?
One of the tests of Quantum Electrodynamics is the value of the "Anomalous magnetic dipole moment".
The theoretical value is:
$$a_e = 0.001\ 159\ 652\ 181....$$
We say that QED "...
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Why are the propagators in old-fashioned QED oblique, while in modern QED they are horizontal (or vertical)?
In old-fashioned Quantum Electrodynamics, one can find diagrams such as these (probably Stückelberg was the first to use this notation, a kind of predecessor of Feynman diagrams):
In modern QED this ...
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Scalar electrodynamics "seagull" vertex factor
By expanding the covariant derivative of the Scalar QED lagrangian one gets the following term, sometimes called "seagull" vertex.
$$\mathcal{L}_{seagull} = -q^2A_\mu A ^\mu \phi^\dagger \phi$$
Most ...
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Proof non-convergence of perturbation in QED
This is an attempt to ask separately about aspects of my previous question, which was closed as too broad. Note that I strongly prefer results that are or can be made mathematically completely ...
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Measuring the Dirac field
If the Dirac field $\psi(x)$ is to the electron as the Electromagnetic field is to the photon, why is it that we can measure the Electromagnetic field, whereas the Dirac field we cannot?
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Is it reasonable to interpret the Lamb shift as vacuum induced Stark shifts?
This is a pretty hand-wavy question about interpretation of the Lamb shift. I understand that one can calculate the Lamb shift diagrammatically to get an accurate result, but there exist "...
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Weinberg Vs Srednicki analysis for the electron self-energy
I am reading Srednicki's book on QFT. Specifically, I am reading about the loop corrections to the fermion propagator (Chapter 62). The relevant expression representing the one-loop and counterterm ...
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Does the Euler-Heisenberg Lagrangian lead to attractive or repulsive interaction between photons?
Photon - photon scattering in QED at low energies can be accurately described by the Euler-Heisenberg effective Lagrangian. This only involves the photons (naturally) because the electron has been ...
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The cross section for production of a fermion-antifermion pair in Peskin and Schroeder (Eq.7.92)
I'm working on the Eq.$7.92$ in Peskin $($page $252)$
I have two questions here：
Question $\bf 1$ : That is just what we would expect from the unitarity relation shown in Fig. $7.6~(\text b)$;
The ...
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EM Field Quantization in Spherical polars
Is it possible to quantize the electromagnetic field in spherical polar coordinates instead of cartesian ones?
Such that creation and annihilation operators correspond to harmonic oscillator modes ...
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What is the effective (quantum) lagrangian of a fermion field for fixed electromagnetic field?
... or, put it another way, what are the loop corrections to the dirac equation in the presence of a fixed (external) electromagnetic field?.
Background
Let $\mathcal L=\frac{1}{2}(\partial\phi^2+m^...
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experiment proposal to validate microcausality
I've been wondering about microcausality for some time now (a recent question of mine regarding the topic) and i'm wondering if its possible to devise an experiment to detect potential violations
I ...
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Spatial wave-function of a single photon and its measurement
In the last decade there were several papers claiming that they've measured a "transverse quantum state" / "quantum wave-function" / "spatial Wigner function" of a single photon:
Measurement of the ...
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Eikonal and soft limits
I am really confused about the difference between the eikonal and soft limits. I am trying to understand how collinear divergences cancel in gravitational scattering amplitudes.
Let me first define ...
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Is the photon propagator always coupled to a conserved current?
I was reading Mandl and Shaw's book on quantum field theory and on page 184 I came across the sentence "the photon propagator always occurs coupled to conserved currents". This allows him to ...
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Has anyone derived a classical radation reaction term directly from QED?
As far as I know, pretty much the only aspect of classical EM that's still actively controversial within the physics community is the best way to treat the radiation reaction force exerted on an ...
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Gauge dependence of Feynman propagator
In QED we have the property that any gauge dependence must cancel out in physical quantities. Nevertheless Feynman rules display some gauge dependence. This is what I am a little unclear on.
The ...
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Scattering, absorption, emission and virtual photons
From reading many questions on this site I have the following conclusions:
Interaction of a photon and a free electron is an instantaneous process of scattering (transfer of momentum) between said ...
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Angular momentum of the Photon
I am reading the QED book by Landau and Lifshitz and I am having a confusion with the angular momentum of a photon.
In the book, they show that the total angular momentum $j$ cannot be zero and takes ...
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Equality of electric charges of all leptons
What does it precisely mean the often repeated statement that the electric charges of all leptons are the same.
Let's consider QED with two leptons: electron and muon. The interaction part of the ...
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When can photon field amplitudes be written as field operators?
Suppose I have some classical field equation for two photon fields with amplitudes $A_1(z),A_2(z)$ (plane waves) given as
${A}_1=\alpha f(A_1,A_2) \\
{{A}_2}=\beta g(A_1,A_2) $
Under what ...
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Can the Lamb shift be expressed in more-or-less closed form in terms of the renormalized 2-, 3-,...,n-point VEVs of QED?
I see here that there are three contributions to the Lamb shift, from vacuum polarization (-27 MHz), from electron mass renormalization(+1017 MHz), and from the anomalous magnetic moment (+68 MHz).
...
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Gauge invariance of 2-to-2 scattering at order $e^4$ in scalar QED
I am trying to show explicitly that the amplitude for the scattering of two scalar particles at order $e^4$ is gauge-independent. The Lagrangian is
$$\mathcal{L}= (D^\mu \chi_1)^\dagger (D_\mu \chi_1) ...
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Is massless QED more "natural" than massive QED?
My understanding is that massive and massless QED share some key physical features including (see this PSE post and 8-4 of Ref. 1):
renormalizability
charge conservation
The key differences of ...
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Source of hierarchy problem for fermions and bosons
In the beginning of a SUSY course, we computed $1$-loop level corrections to the mass of a bosons $\phi$ and a fermion $\psi$ in the theory
\begin{align}
\mathcal{L} &= \bar{\psi}(i\gamma^\mu D_\...
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Huygens principle and path integral for classical waves
I want to better understand what the path integral is and what it isn't.
Even though I do this to learn QFT, this question is purely concerned with classical fields, no quantization is intended at all....
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Spinor Helicity Formalism: Reference Spinors $q$ in Compton Scattering
My question is rather straight forward, but the setup in order to pose the question is a little lengthy; please bear with me!
I am trying to calculate the average over initial states and sum over ...
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Vacuum polarization or electron with structure?
Is it possible to construct some charge density $ρ(r)$ to get the Uehling-Potential?
$${\displaystyle V_{\text{Uehling}}(r)\approx -Z\alpha \hbar c{\frac {1}{r}}\left(1+{\frac {\alpha }{8\pi ^{2}{\...
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Intuitive microscopic explanation of Lenz's Law?
Consider a horizontal wire loop through which a magnet is dropped. I understand the macroscopic explanation. The moving magnet generates an electric current in the wire loop(counterclockwise when ...
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Some questions about generalized symmetries
The topic of generalized symmetries is rather new, as far as I understand, the first paper on them was - https://arxiv.org/abs/1412.5148. And I would like to grasp a deeper understanding of them. ...
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Verify Furry theorem in scalar QED
I want to verify Furry theorem in scalar QED. Consider a process with N photons. Is it correct to say that at 1 loop the two classes of Feynman diagram that contribute are the following?
with $n+2m = ...
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Relation between the trace anomaly and the energy-momentum tensor being off-shell
Let's say we have a massless QED theory with a Lagrangian
\begin{equation}
L=i\bar{\psi}\not{D}\psi-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}
\end{equation}
The symmetric energy-momentum tensor is
\begin{...
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Do longitudinal and scalar have anything to do with Faddeev-Popov ghosts?
In his this book, Hatfield calls ghosts the negative states appearing in the covariant (Gupta-Bleuler) quantization prescription of the electromagnetic field (page 89). When discussing Yang-Mills ...
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Contact terms in derivation of Ward identity
(This post is a bit long; the key question is between the horizontal lines, and an example follows it.)
I am following the derivation of the Ward identity in Schwartz's QFT book, and there is a key ...
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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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The Purcell effect, it's influence on the lifetime and quantum yield (of fluorophores)
So I've been looking into the Purcell effect and how it interacts with fluorophores (fluorescent molecules). The Purcell arises when you have a dipole in a cavity or even just near a dielectric or ...
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What is the problem of non-pertubative quantisation?
In reading books about quantisation, there is (sometimes hidden) the claim, that quantisation is done using a pertubative approach. You look at the free field, find that it is essentially a sum of ...
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Spin vs Helicity conservation
I am a bit confused about spin conservation at relativistic energies. I am reading a QFT book by Peskin and at a point he specifies that "In the nonrelativistic limit the total spin of the system is ...
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Is the physical mass of the electron a gauge invariant quantity?
In Lattice, one cannot calculate gauge non-invariant quantities, such as the quark mass. This is because one averages over the gauge and gets 0.
One way to get around the issue is to fix the gauge. ...
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Feynman rule for closed fermion loop in QED
One of the Feynman rules of QED is the following:
For a closed fermionic loop, the Feynman rule is to start at an arbitrary vertex or propagator, follow the line until we get back to the starting ...
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Commutation of currents in QED
In an outline of a proof of the Ward identities in QED, the authors Green, Schwarz, and Witten in their book "Superstring theory", vol. I, Section 1.5.1,
claim that in the QED the ...
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Gauge invariance and the unitarity
I want to discuss the relation between the unitarity and the gauge invariance. Suppose we have for simplicity an abelian gauge theory (say, EM theory). We want to quantize it in terms of 4-potential $...
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