All Questions
91
questions
1
vote
0
answers
173
views
Explicit counting of gauge field degrees of freedom
Consider a connection on a principal $U(1)$-bundle $A_\mu$ over the flat base manifold $M_4$. The action of the theory is described in terms of the curvatures of such connection coupled to some source ...
- 195
2
votes
1
answer
319
views
Landau levels in symmetric gauge
On Shankar’s Quantum Many body page 394 it says for one electron in a magnetic field, ignoring spin,
$$H_0=\frac{(\bf{p}+e\mathbf{A})^2}{2m}$$
$$e\mathbf{A}=-\frac{\hbar}{2l^2}\hat{z}\times \mathbf{...
- 301
1
vote
0
answers
149
views
Why is the Coulomb Gauge enough to fix extra degrees of freedom?
In classical electrodynamics, we have after the Coulomb gauge is applied:
$$ \Delta U = -\frac{\rho}{\epsilon_0} $$
$$ \Box \vec{A} = \mu_0 \vec{j}-\frac{1}{c^2} \vec{\nabla} \frac{\partial U}{\...
- 1,450
0
votes
1
answer
133
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How do I show that the Lorenz gauge is consistent?
I have been asked to show that the Lorenz gauge condition, written as
$$\nabla_T \bullet \vec{A} + \dfrac{1}{c^2}\dfrac{\partial}{\partial t}\Phi = 0$$ is mathematically consistent with the vector ...
2
votes
1
answer
636
views
Why Coulomb gauge is a possible gauge choice?
In classical field theory we can get, that adding gradient of some scalar field to magnetic vector potential does not change the physics at all. So, we have such a symmetry:
$\boldsymbol{A}\...
- 331
1
vote
1
answer
255
views
Is any other gauge ever more useful than Lorenz gauge for practical calculations in classical EM?
Any problem in gauge theory can of course in principle be solved in any gauge (or, in the case of classical gauge theory, without using gauge potentials at all), but some gauges are much more useful ...
- 48.4k
1
vote
1
answer
340
views
Quick question on choosing a gauge (E.g. Lorenz gauge)
I have been quite confused when I read about choosing a gauge. For example we have the gauge transformation
$$
A_\mu\longrightarrow A_{\mu\prime}= A_\mu+\partial_\mu\alpha,
$$
and we can choose any $...
- 302
1
vote
3
answers
378
views
Why does gauge invariance in electrodynamics mean that there are redundant degrees of freedom? [closed]
It is possible to choose different gauges in electrodynamics. I am familiar with two of them: Coulomb gauge and Lorenz gauge. Let us stick to the Coulomb gauge. It sets $$\nabla\cdot\vec{A}=0.$$ The ...
- 11.8k
2
votes
2
answers
702
views
Gauge Invariance in Electrodynamics
I am studying Electrodynamics and I have been introduced to the concept of Gauge Invariance.
This was introduced by noting that $E$ and $B$ amount to 6 six degrees of freedom and the Maxwell ...
- 1,094
4
votes
5
answers
949
views
Is fixing the gauge the same thing as performing a Lorentz transformation?
Let's say I have a moving charged particle, with constant velocity.
Its electric field is given by (generally):
$$ \mathbf{E} = -\nabla\phi - \frac{\partial \mathbf{A}}{\partial t}. $$
If I perform ...
- 24.9k
0
votes
3
answers
3k
views
What is the Lorenz condition for potentials?
I was just going through the "Electromagnetic Waves" chapter in the Classical Field Theory book by Landau. Here he mentions that they impose an auxiliary condition and it is known as the Lorenz ...
- 61
5
votes
1
answer
1k
views
Residual gauge fixing in Lorenz gauge
Background
Let $A^{\mu}$ be a 4-potential that satisfies the Lorenz condition
$$\partial_\mu A^\mu =0$$
We can make a gauge transformation $$A_\mu \to A'_\mu=A_\mu + \partial_\mu \Lambda$$
such that
$...
- 430
3
votes
2
answers
680
views
EM field in a vacuum in terms of potentials
I know we can express the electric field $\mathbf{E}$ and the magnetic field $\mathbf{B}$ in terms of the electric potential $\phi$ and vector potential $\mathbf{A}$:
$$ \mathbf{E} = -\nabla \phi - \...
- 3,986
2
votes
1
answer
692
views
Quantum particle on a ring with magnetic flux through it: Can we gauge away the magnetic field?
Consider a quantum particle on a ring and a non-zero homogeneous magnetic field perpendicular to the disk that the ring defines and is non-zero only in the inside of the perimeter of the ring. Let $\...
- 7,720
3
votes
3
answers
2k
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Physical meaning of gauge choice in electromagnetism
In electromagnetism, it is often referred to gauges of the electromagnetic field, such as the radiation or Coulomb gauge. As far as I know, the definition of a gauge helps us to redefine the problem ...
- 1,764