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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Is there any radiation similar to Bremsstrahlung in electron-electron or electron-positron scattering?
When an electron scatters on a nucleus, it emits Bremsstrahlung, which makes sense as any charge being accelerated emits EM radiation.
However, I don't remember free electrons emitting any radiation ...
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What determines how wide are the absorption spectrum lines of atoms?
So let's assume we have atoms in their ground state and we measure what kind of wavelengths those atoms can absorb. These should occur at photon energies that correspond the the energy gaps between ...
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Underlying correspondence of calculating the imaginary part of the effective Lagrangian in sQED
I was wondering if there is a correspondence/underlying equivalence between the heat kernel, tunnelling, and Bogolubov approaches for calculating the imaginary part of the effective Lagrangian in sQED ...
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Functional derivative of gauge fixing condition - Peskin QFT page 295
In Peskin QFT book page 295 it is said that:
$$\det(\delta G(A^\alpha)/ \delta \alpha) = \det(\partial^2/e)\tag{p.295}$$
where $$G(A^\alpha) = \partial^\mu A_\mu^\alpha = \partial^\mu A_\mu + (1/e)\...
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Can photons be seen in a superconductor?
In the video Electromagnetism as a Gauge Theory, Richard Behiel states that electromagnetism is a result of adding local phase symmetry to the Dirac equation. He also says (at 3h9m) that this phase ...
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Pole structure of the photon polarisation tensor
When it comes to the photon polarisation tensor in the book of Peskin & Schroeder on page 246, it is said:
Notice that as long as $\Pi(q^2)$ is regular a $q^2=0$, the exact propagator always has ...
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Phase Space Integral For Compton Scattering COM Frame
I have a question about how to compute the phase space integral for Compton scattering in the COM frame. I was following Peskin and Schroeder Introduction to Quantum Field Theory. They have the ...
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Relativistic corrections to Mandelstam variable $t$
a book (Quantum Electrodynamics by Akhiezer and Berestetskii, 2nd ed. pp. 522) claims that when evaluating a Feynman diagram for Moller scattering, the $\frac{1}{q^2}$ in the matrix element $(\bar{u}_{...
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Is there a path integral expression for the Anomalous magnetic dipole moment?
I'm wondering how you might express the magnetic moment of the electron:
$$a_e = \frac{\alpha}{2\pi} + \mathcal{O}(\alpha^2) $$
In terms of a ratio of Feynman path integrals.e.g. something involving ...
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Are Stokes parameters Lorentz invariant?
Are the Stokes parameters for polarization relativistic? i.e. Lorentz invariant? And if it is so, then how to show it?
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Are angular momentum selection rules only understood for hydrogen like species?
I am someone with a rudimentary understanding of atomic and molecular physics, and with that I'm trying to understand in which case which selection rule becomes applicable. For the angular momentum ...
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Question about fermion self-energy and on-shell renormalization
Assume that we calculate $i\Sigma(\not{p})$ in Eq. (62.28) in Srednicki's book on QFT. If $p$ is the momentum of an external massive particle of mass $m$, then the equation
$$\not{p}=-m$$
holds. In ...
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How does photon exchange create an attractive force? (electromagnetism) [duplicate]
excuse my classical way of thinking, but how is it that electromagnetism (or any other fundamental force that is mediated by particules) can be an attractive force, yet work by exchanging photons, and ...
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What is the status of Wheeler’s ‘one-electron universe’ idea? [duplicate]
I'd like to ask the experts about the following:
Sometime ago, I read about the One-electron universe postulate by Wheeler, and I found the concept fascinating. I wonder if it is a line of work that ...
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If electrically charged particles transact virtual photons, why aren't said virtual photons subject to the rules of general and special relativity?
For instance, if there exists an electron at sea level, and an electron in orbit, why don't the virtual photons which mediate their electrical field contract and expand as they move across the ...
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Calculate scalar QED vertex using LSZ formula
I am self-studying QFT using the Schwartz book "Quantum field theory and the standard model", and I am reading chapter 9 about Scalar QED.
I am trying to calculate the following vertex using ...
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Atomic off-resonance absorption in a full quantum theory
When studying atomic absorption in time-dependent theory, we learn (see, for example, Griffiths, 1Ed, pg. 307), that the probability of absorption is given by,
$P_{a\rightarrow b}(t) \propto \frac{\...
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Vertex Feynman rules for scalar QED
I am self-studying QFT using the Schwartz book "Quantum field theory and the standard model", and I am reading chapter 9 about Scalar QED.
At page 143 he shows the fours possible vertex (at ...
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Why this family of Hamiltonian being introduced when dealing with system under Periodic Boundary Condition?
While studying the large system under periodic boundary conditions, a family of Hamiltonian is introduced which is ,
$\hat{H}(\alpha) = \frac{1}{2m} \sum_{i=1}^{N} {(p_i -\hbar\alpha)}^2+ \hat{V}$
$\...
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When can you neglect terms like $a_n a_{n+1}$ or $a_n^\dagger a_{n+1}^\dagger$? [duplicate]
I am looking for a detailed explanation of when and why we can neglect terms like $a_n a_{n+1}$ or $a_n^\dagger a_{n+1}^\dagger$ in Hamiltonians like
$$
H = \omega \sum_n a^\dagger_n a_n + \lambda\...
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String Electrodynamics - Need Some References
I am very interested in the intersection between String Theory and Electrodynamics - classical or quantum. What are some good books, scientists, articles or even discussions that can give me more of ...
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Is there a liquid Scharnhorst effect generalizing the liquid Casimir effect?
Context:
This question originates as a generalization of this. The Casimir effect is an attraction between two conducting plates predicted by QED due to the exclusion of certain virtual photon ...
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Are Greens function infrared finite in QED?
Scattering amplitudes are infrared divergent in QED, but are Greens functions infrared finite or infrared divergent. e.g. Is the four-point function
$G(x_1,x_2,x_3,x_4)=\langle\Omega|T \Big(\bar{\psi}(...
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What is the maximum amount of energy one electron can have? [closed]
Is there any limit on the amount of energy one free electron can have?? Certainly there should be a limit. I think High Energy Physics should be able to answer it. Please somebody help.
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Can you introduce nuclei into QED as elementary particles with charge $+Ze$?
If we'd like to look at the interaction between nuclei and electrons using QED - e.g., let's say we want to describe the hydrogen molecule - could we introduce the hydrogen nuclei as another "...
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Euler-Heisenberg Lagrangian & heat kernel: Why do we need to substitute $s \to -is$ to continue calculating?
Starting from the general effective lagrangian for a constant background electromagnetic field,
$$\mathcal{L}_{\mathrm{EH}}=-\frac{1}{4}F_{\mu\nu}^{2}-\frac{e^{2}}{32\pi^{2}}\int_{0}^{\infty}\frac{ds}{...
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How many significant digits could the fine structure constant have?
The fine structure constant 1/137,035999... (at low 4-momentum) is a famous quantity of nature.
How many significant digits could it have?
More specifically, could it have more than 62 significant ...
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Schwinger approach using the heat kernel [closed]
I am having trouble calculating the effective action for a constant magnetic background. The calculations I am trying to replicate are from this paper: https://arxiv.org/abs/hep-th/9807031. The ...
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Linear response theory for emissions
Is it possible to study emissions via linear response consider an external electromagnetic field emission $A^{\mu}$ studied via the interaction
$$H_{int} = g\int d^4x ~\bar{\psi}\gamma^{\mu}\psi A_{\...
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Why do IR divergences only appear on external legs of a Feynman diagram in the discussion of Bremsstrahlung?
On p. 203 in section 6.5 of Peskin and Schroeder, the diagrams below are given as examples of when an infrared divergence occurs.
'Soft photons' are photons with energy below some cutoff that we ...
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Wave-particle duality: interactions of like / different quantum fields
With my pop-sci level of understanding, it seems to me that quantum fields exhibit particle-like properties only when interacting with a different quantum field - i.e. electromagnetic field interacts ...
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Resources with treatment of Quantum Optics as an application of Quantum Field Theory?
I am looking for resources which deal with Quantum Optics, with some rigor, as an application of Quantum Field Theory.
PS:I have read Introductory Quantum Optics by Gerry and Knight. So that is my ...
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What is the proper ansatz for describing an electron-photon many-particle System?
I am somewhat used to simplified non-relativistic quantum mechanics (both canonically and grand canonically), describing a system by a Hamiltonian containing a kinetic part, an external potential as ...
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Does vacuum polarization strengthen or weaken the electric field emitted from a proton?
I’m currently reading Rafelski and Muller’s The Structured Vacuum, and I’m a little confused by something they’re saying. I wouldn’t exactly call this a pop-physics book, but it’s pop-ish, so it’s ...
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Why is PDC radiation someties emitted as a hollow cone and sometimes appears as a 2D gaussian?
Common depictions of PDC radiation depict it as a hollow cone being emitted. In the imaging plane, this then appears as a circle. See for example the following picture from this arXiv upload:
On the ...
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Why do we treat quadratic counterterms as interactions rather than free terms? [duplicate]
For example, in QED (or any other theory containing particles with spin 1/2) the renormalized countains
$$
\mathcal{L} \subset \bar{\psi} (i \displaystyle{\not}\partial -m)\psi + \bar{\psi} (\delta_2 ...
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Odd notation $\stackrel{\leftarrow}{\nabla}$ for a gradient
I've tried working out the Heisenberg EOM for the 4-current operator. Two very beautiful articles (DOI: 10.1103/PhysRevA.84.042107, DOI: 10.1103/PhysRevA.90.012508) present this result, but I have not ...
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Rewrite 3-loops in simpler integrals
I am working with the following integral, similar to the "setting sun'' diagram by Pierre Ramond in his QFT book:
\begin{equation}
\int \frac{d^dp}{(2 \pi)^d} \int \frac{d^dk}{(2 \pi)^d} \int \...
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What happens with direct electron-muon couplings?
Checking Peskin's Intro to QFT book, I found the following mantra, when talking about the interaction Hamiltonian $H_I$ obtained throught the expression $\langle\mu^+\mu^-|H_I|e^+e^-\rangle$:
our ...
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How/Why is pair annihilation accounted/permitted in QED?
Following Schwartz Intro to QFT, I understand that through the introduction of virtual off-shell particles, we can allow fermion anti-fermion annihilation vertices to exist in QED, as long as the ...
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Charge renormalization Only Arise From Radiative Correction to the Photon Propagator
In Weinberg's QFT V1 section 10.4, he say that there is only radiative corrections to the photon propagator contributing to the charge renormalization, and other radiative corrections to the ...
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How to find two-point correlators of field strength in Maxwell theory?
I know $\langle A_\mu \rangle=0$ by Lorentz symmetry. Here the expectation values $\langle . \rangle$ are taken w.r.t. the vacuum. Taking derivatives we have $\langle F_{\mu \nu} \rangle=0$. This ...
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Coulomb Potential in Bhabha (fermion + anti-fermion) scattering
In computation of Coulomb potential of Bhabha (fermion + anti-fermion) scattering in Peskin and Schroeder QFT section 4.8 eq. (4.136), they only consider one Feynman $t$-diagram without claiming the ...
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Deriving Feynman rules for QED using the path integral
The Lagrangian for QED is
$$\mathcal{L} = \bar{\psi}(i\displaystyle{\not}\partial -m)\psi - \frac14(F_{\mu\nu})^2 - e\bar{\psi}\gamma^\mu\psi A_\mu = \mathcal{L}_0 - e\bar{\psi}\gamma^\mu\psi A_\mu.$$
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Questions about QED Corrections to Coulomb's law and Electromagnetic Wave Equation
As a disclaimer, this is somewhat similar to this unanswered question, but not entirely.
In standard QED theory, it is frequently demonstrated that the derivation of the Coulomb Potential can be found ...
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Photon Mass Regulator in IR divergences
On Schwartz's QFT page 333, he metions that there is infrared divergence when we try to renormalized the two-point function of electron field in on-shell substraction scheme,
$$\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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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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