All Questions
91
questions
1
vote
1
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425
views
Gauge fixing in the classical $U(1)$ gauge theory
My question concerns the gauge fixing in classical v.s. quantum $U(1)$ gauge theory. I will ask about the gauging fixing in quantum $U(1)$ gauge theory in a separated Phys-SE post.
For the classical $...
- 4,336
1
vote
1
answer
318
views
Quantisation of gauge field in temporal gauge
Whenever we use temporal gauge and quantise gauge field we implement Gauss law. I have seen some papers but the point is not cleared to me that why we implement Gauss law there. Please explain this if ...
- 43
1
vote
1
answer
203
views
When we use Lorenz gauge or Coulomb gauge, the result formula for electric $E$ and magnetic field $B$ is same or different?
Gauge condition can be chosen as you like or not?
is the Lorenz gauge is the only one correct? If Coulomb gauge can obtained exactly same results as Lorenz gauge for the electromagnetic fields E and ...
- 149
1
vote
1
answer
180
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Photon Path Integral and Lorenz Gauge
I am reading Srednicki's QFT book (http://web.physics.ucsb.edu/~mark/qft.html). In chapter 57, specifically in page 343, the book stated that there's a problem with the path integral because the ...
- 673
1
vote
1
answer
153
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Gauge transformation of the gauge-fixing term in the QED action
In the classroom my teacher stated that the Gauge-fixing term in the action
$$\frac{1}{2\alpha}\int d^4x (\partial_\mu A^\mu(x))^2$$
transforms under $A_\mu(x) \rightarrow A_\mu(x)+\partial_\mu \...
- 99
5
votes
1
answer
1k
views
$R_\xi$ gauges and the EM-field
$R_\xi$-gauges are said to be a generalization of the Lorenz gauge. I dont quite get why we add the term
$$
\mathcal L_{GF} = - \frac{(\partial_\mu A ^\mu)^2}{2\xi}\tag{1}
$$
to the Lagrangian. If i ...
- 2,196
2
votes
2
answers
504
views
Gauge invariance for classical fields
I recently did some exercises in classical field theory and tried to think deeply about the gauge symmetry of the free electromagnetic field described by the Lagrangian
$$
\mathcal L = -\frac 1 4 F^{\...
- 2,196
0
votes
1
answer
186
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What are all the gauge symmetries & derivatives of the QED lagrangian?
I find that the gauge symmetries of the lagrangian are a topic that gets obfuscated quite a bit. I'm trying to understand the big picture of this in QED. My understanding is that:
Gauge derives its ...
- 1,427
1
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1
answer
249
views
For the free electromagnetic field, is it possible make single gauge transformation to achieve $\phi={\bf \nabla}\cdot{\bf A}=0$?
For any electromagnetic field, it is easy to impose the Coulomb gauge condition ${\bf\nabla}\cdot{\bf A}=0$. To start with, if ${\bf \nabla}\cdot{\bf A}_{\rm old}\neq 0$, the trick is to make a gauge ...
- 26.8k
7
votes
1
answer
744
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Why is the gauge-fixing condition squared in the QED Lagrangian?
Consider the free Maxwell Lagrangian:
$$L= -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}. $$
As we know, the gauge symmetry $A_{\mu} \rightarrow A_{\mu}+\partial_\mu \lambda$ must be fixed when quantizing the ...
- 2,296
1
vote
1
answer
113
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Quantisation of gauge theory with minimal coupling
I have a question on the quantization of the gauge theory with minimal coupling term. What I understand is that if one is given an action
$$
S=-\int d^4 x \frac{1}{4}F^2 \tag1
$$
Since this action has ...
- 311
1
vote
2
answers
1k
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How does gauge-fixing really work?
Leaving technical issues like Gribov copies and residual gauge freedom aside, how do gauge fixing conditions like the Coulomb condition
\begin{equation}
\partial_i A_i =0
\end{equation}
or the axial ...
- 10.1k
6
votes
1
answer
1k
views
Why does Coulomb gauge condition $\partial_i A_i =0$ pick exactly one configuration from each gauge equivalence class?
There are infinitely many configurations of a vector field $A_\mu$ that describe the same physical situation. This is a result of our gauge freedom
$$ A_\mu (x_\mu) \to A'_\mu \equiv A_\mu (x_\mu) + \...
- 10.1k
5
votes
4
answers
1k
views
Why does Lorenz gauge condition $\partial_\mu A^\mu =0$ pick exactly one configuration from each gauge equivalence class?
For a vector field $A_\mu$, there are infinitely many configurations that describe the same physical situation. This is a result of our gauge freedom
$$ A_\mu (x_\mu) \to A'_\mu \equiv A_\mu (x_\mu) + ...
- 10.1k
2
votes
1
answer
143
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What is a gauge (for someone who has not studied gauge theory)? [duplicate]
I am taking a Quantum Mechanics II course and we were studying the relativistic corrections to the hydrogen atoms in perturbation theory. I was looking at the assignment, and a question is as follows: ...
- 538