All Questions
91
questions
1
vote
0
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267
views
How to find Weyl/temporal gauge fixing condition?
Transformations that leave the field invariant:
$$\vec{A}' = \vec{A} + \nabla f$$
$$\phi' = \phi -\frac{\partial f}{\partial t}$$
I would like to solve for the weyl gauge, aka a gauge that leaves
$$\...
- 6,636
1
vote
1
answer
199
views
What is 't Hooft-Veltman gauge? What are the interactions in SM in 't Hooft-Veltman gauge?
What is 't Hooft-Veltman gauge? I can't really find any suitable answer online. If we introduce this gauge in SM, then what becomes interactions?
- 23
0
votes
0
answers
64
views
Steps in Quantizing Electromagnetic Field for the Gauge Condition $A_0=0$
While reading section 9.3 of QFT An Integrated Approach by Fradkin, it is shown (see equations $(9.49)$ and $(9.54)$ of the book)
$$B_{j}(\boldsymbol{x})^{2}=\boldsymbol{p}^{2} A_{j}^{T}(\boldsymbol{p}...
- 381
-1
votes
2
answers
667
views
Coulomb gauge with $\rho = 0$ implies Lorenz gauge?
Maxwell equations take the form:
$$\nabla^2 \phi + \frac{\partial}{\partial t} \nabla \cdot \vec{A}= - \frac{\rho}{\epsilon_0}\qquad (\nabla^2 \vec{A} - \mu_0\epsilon_0\frac{\partial^2 \vec{A}}{\...
- 6,636
0
votes
0
answers
65
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The choice of gauge seems has contradiction
Suppose I have a quantum object, inside it the electric field distribution is $\vec{E}(\vec{r})$, with this field we can obtain the scalar potential $\phi(\vec{r})$, a charged particle in this object ...
- 6,095
1
vote
2
answers
203
views
Existence of the Coulomb gauge
In reading about the Coulomb gauge, my mind seems to have painted itself into a corner. For, lets assume that Maxwells equations for the physics of the problem are solved by the magnetic vector ...
- 446
2
votes
1
answer
543
views
Do the retarded potentials satisfy the Lorenz Gauge condition?
Every source I have ever seen derives the retarded and advanced potentials by finding the Green's functions of the inhomogeneous Lorenz gauge conditions, and I have always thought that any linear ...
- 269
1
vote
1
answer
110
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Transforming the potentials that satisfy Lorenz & Coulomb gauge to potentials that satisfy only Lorenz gauge
If $\vec E(\vec r,t)=\vec E_0sin(\vec k \vec r- \omega t)$ and also that $\rho(\vec r,t)=0$ and $\vec j(\vec r,t)=0$
I was asked to find $\vec A(\vec r,t)$ and $\phi (\vec r,t)$ which satisfy both the ...
- 1,398
0
votes
1
answer
72
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Lorenz Gauge different definitions
For the lorenz gauge we can either write:
$$\nabla \vec A(\vec r,t)+\frac{1}{c^2}\frac{\partial \phi(\vec r,t)}{\partial t}=0$$
If we also consider the following invariant transformations:
$$\vec A(\...
- 1,398
1
vote
2
answers
286
views
Coulomb Gauge misunderstanding
If we have $\vec A(\vec r,t)$ and $\phi (\vec r,t)$ and we make the following gauge transformations:
$$\vec A(\vec r,t)'= \vec A(\vec r,t) + \nabla f(\vec r,t)$$
$$\phi(\vec r,t)'=\phi(\vec r,t) - \...
- 1,398
2
votes
2
answers
207
views
"One-parameter" gauge transformation
In my advanced classical physics course, it was stated that the electromagnetic field strength tensor $F_{\mu\nu} = \partial_{\nu}A_{\mu} - \partial_{\mu}A_{\nu}$ is invariant under "one-...
- 234
1
vote
0
answers
31
views
Gauge fixing terminology (math terms) [duplicate]
In the majority of the sources I've read regarding gauge fixing, the authors sometimes use (IMHO) a vague terminology. Let's take the case of the magnetic vector potential $\vec{A}$ defined as
$$ \vec{...
- 149
0
votes
1
answer
140
views
Gauge invariant Green's function for a point particle
This question is a follow up to the question (Gauge invariant Green's function for electrodynamics).
It is not possible to generally solve the eqution
\begin{equation}
\square A^{\mu}-\partial^{\...
- 498
2
votes
2
answers
214
views
Gauge invariant Green's function for electrodynamics
Varying the electromagnetic action
\begin{equation}
S=-m c \int d s\left(\dot{z}^{2}\right)^{\frac{1}{2}}-\frac{e}{c} \int d s A_{\mu} \dot{z}^{\mu}-\frac{1}{16 \pi c} \int d^{4} x F_{\mu \nu} F^{\mu \...
- 498
5
votes
1
answer
940
views
Gauge symmetry of massive vector field
Consider a real massive vector field with lagrangian density
$$\begin{align}\mathcal{L}&=-\frac{1}{4}(\partial_\mu A_\nu-\partial_\nu A_\mu)(\partial^\mu A^\nu-\partial^\nu A^\mu)+\frac{1}{2}m^2 A^...
- 2,284