All Questions
91
questions
0
votes
2
answers
638
views
Coulomb gauge in special relativity (for QFT)
I don't totally understand the procedure of Coulomb Gauge that we do in special relativity.
Here is what I understood.
We have: $$ F_{\mu \nu}=\partial_{\mu} A_{\nu} - \partial_{\nu} A_{\mu}$$
It ...
- 1,450
0
votes
1
answer
960
views
Gauge fixing with vector potential: Coulomb gauge
There is something I would like to clarify with gauge fixing.
In E.M, we can introduce the potential vector.
As $div(\vec{B})=0$ we know that we can write $\vec{B}=\vec{curl}(\vec{A})$.
But as $\...
- 1,450
1
vote
1
answer
276
views
In simple words, why does a Lorenz Gauge does not have any physical effects?
I'm studying vector calculus via Arfken & Weber's "Mathematical Methods for Physicists", and, in page 40, he is deriving the electromagnetic wave equation.
During the demonstration he states that ...
- 501
10
votes
1
answer
3k
views
Gauge theory and eliminating unphysical degrees of freedom
In free space we can express Maxwell's equations as
\begin{align}
\varepsilon^{abcd}\partial_bF_{cd}=0 ~~\text{ and }~~ \partial_aF^{ab}=0 \tag{1}
\end{align}
where $F^{ab}=-F^{ba}$. The most general ...
- 599
10
votes
2
answers
2k
views
Question about physical degree of freedom in Maxwell Theory: Why Coulomb gauge can fix all redundant degree of freedom
Given $4$-potential $A^\mu(x)=(\phi(x),\mathbf{A}(x))$, the vacuum Maxwell equations:
$$\nabla^2\phi+\frac{\partial}{\partial t}(\nabla\cdot \mathbf{A} )=0$$
$$\nabla^2 \mathbf{A} -\frac{\partial^2 \...
user153663
2
votes
1
answer
656
views
Ensuring Lorenz Gauge condition in Green Function solution
In the Lorenz Gauge, we can write Maxwell's equations as:
$$\tag1 \Box A^\beta=\mu_0j^\beta.$$
We then go on to solve this by treating each component $A^\beta$ as an independent solution of the ...
- 1,836
3
votes
1
answer
583
views
Quantization of a spin-1 field canonical commutator
This is a question regarding the spin-1 massive field commutator $[A_i(\mathbf{x},t),\Pi_j(\mathbf{y},t)]$, where $\Pi$ is the conjugate field and $A^\mu$ is the four-potential. My result was,
$$[A_i(\...
- 63
1
vote
1
answer
167
views
How do gauge transformation imply gauge conditions?
In classical EM I understand the electric and magnetic fields are invariant under the potential transformations $\varphi\to\varphi - \partial_t\chi$ and $\mathbf{A}\to\mathbf{A} + \nabla\chi$.
From ...
- 500
3
votes
1
answer
985
views
Laplacian of Lorenz gauge magnetic potential
My textbook, Gettys's Physics (Italian language edition), says that the Lorenz gauge choice uses the magnetic vector potential $$\mathbf{A}(\mathbf{x},t):=\frac{\mu_0}{4\pi}\int \frac{\mathbf{J}(\...
5
votes
3
answers
1k
views
How fundamental is the transversality condition in QED?
This question is probably answered somewhere in textbooks, but I haven't got there yet, sorry for my ignorance in advance.
There is a famous transversality condition in E&M and QED
$$\vec{k}\...
- 1,184
2
votes
1
answer
2k
views
Residual Gauge Freedom [closed]
How are we still left with one Residual Gauge Freedom in the choice of Electromagnetic Potential after having already exploited the Gauge Freedom once.
As is mentioned in Halzen and Martin Section 6.9....
- 169
2
votes
1
answer
440
views
Electron photon interaction - commutation of $\mathbf{A}$ and $\mathbf{p}$
I'm trying to figure out the radiative transition rates between electronic levels due to EM radiation using FGR as done by Merzbacher, this online source, and others.
I have two questions regarding ...
- 695
6
votes
1
answer
2k
views
Why not use the Weyl/temporal gauge?
In E&M in Minkowski space, the Lorenz and Coulomb gauges are typically used since they make things vastly simpler. On a curved background, Maxwell's equations (without sources) can be written as:
\...
- 513
11
votes
2
answers
12k
views
What is the physical meaning of Lorenz gauge condition? [closed]
What is the physical meaning of Lorenz gauge condition?
And what part of the solutions we throw?
- 163
9
votes
3
answers
1k
views
Why do we use gauges in Maxwell equation?
While solving the Maxwell's equation we often use the Lorenz or Coulomb gauge, but why is that? Are the equations unsolvable if the gauge is not fixed? Or is it just for the simplicity?
- 340