All Questions
Tagged with quantum-electrodynamics gauge-theory
128
questions
3
votes
1
answer
58
views
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 ...
- 863
0
votes
0
answers
37
views
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 \...
- 29
3
votes
0
answers
74
views
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
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
- 51
0
votes
0
answers
81
views
Quantizing the electric field without quantizing vector potential
I am trying to quantize the electromagnetic field, without using the vector potential. I start with a Fourier expansion:
$$\begin{equation}
\vec{E}(\vec{r},t) = \sum_{\epsilon} \vec{\epsilon} \int \...
- 1,258
1
vote
1
answer
147
views
How particles interact with the electromagnetic potential $A^\mu$?
It is well known that one reason quantum mechanics started to being developed, was because scientist wanted a model to explain electron orbits in atoms.
Borh interpreted that the for orbits to exist ...
- 1,525
0
votes
0
answers
48
views
Ward identity in scalar QED; gauge transformations & plane wave solutions for polarization
I am prepping for my QFT2 exam tomorrow, and in one of the mock exams I found the following question (and I'm not quite sure how to go about this). Given the following Lagrangian:
$$
L = -\frac{1}{4}...
2
votes
1
answer
94
views
Why are these terms not present in the QED Lagrangian?
I am working though some questions for my QFT/ QED exam and i am having trouble with the following question:
Explain why the following terms cannot be part of the Lagrangian of QED:
$-g(\bar{\psi}\...
- 35
2
votes
1
answer
143
views
Spontaneous Symmetry Breaking, Vacuum Degeneracy, and Goldstone Bosons applied to large gauge transformations
I am reading Strominger's lecture notes on the infrared structure of gravity and gauge theory. I am trying to understand subchapter 2.11, where the author focuses on the notions of "Spontaneous ...
- 3,992
0
votes
0
answers
98
views
Why is the source of the EM Field in QED the probability current and not the electric current?
I have some problems understanding the interaction term in the QED Lagrangian. If we take
$$
\mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \bar \psi (\gamma^\mu\partial_\mu-m)\psi+\bar \psi \gamma^\...
- 29
1
vote
0
answers
50
views
Bibliography for the Quantization of the free electromagnetic field with the Lorenz gauge
Recently I have been studying QFT and when I arrived at the Gauge theory I learned that one can quantize the electromagnetic field with the Coulomb gauge and the Lorenz gauge.
Regarding the Coulomb, I ...
0
votes
0
answers
56
views
What sort of QED-like theories can have non-quantized charge?
It is often said that the existence of a single monopole would force electric charge to be quantized, due to Dirac's argument. However, one can write down theories like QED that, independently of the ...
- 858
1
vote
1
answer
142
views
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 ...
- 61
2
votes
1
answer
162
views
Physical states in Gupta-Bleuler quantization
I'm reading Timo Weigand notes for Gupta-Bleuler quantization of free EM field.
On page 109, Author has made the following statements.
The Gupta-Bleuler condition for physical state is
$$|\vec{p},\...
- 69
3
votes
0
answers
81
views
Is there a way to visualise / understand intuitively the curvature in the $U(1)$ circle bundle responsible for the electromagnetic force?
In general relativity we have embedding diagrams of different slices of spacetimes. These can be quite helpful to understand the geometry of a given pseudo-Riemannian manifold (especially when the ...
- 51
1
vote
1
answer
69
views
Gauge invariance in QED with just fermion transformations
I've got myself confused about a basic question. If we have a gauge-invariant operator $\mathcal{O}$ whose expectation value is
\begin{equation}
\left\langle\mathcal{O}\left(x_1, \ldots, x_n\right)\...
- 841