All Questions
24
questions
18
votes
2
answers
3k
views
Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics
How do I definitively show that there are only two propagating degrees of freedom in the Lorenz Gauge $\partial_\mu A^\mu=0$ in classical electrodynamics. I need an clear argument that
involves the ...
- 6,381
17
votes
3
answers
8k
views
What is a gauge in a gauge theory?
As I study Jackson, I am getting really confused with some of its key definitions. Here is what I am getting confused at. When we substituted the electric field and magnetic field in terms of the ...
- 1,355
10
votes
2
answers
3k
views
Showing that Coulomb and Lorenz Gauges are indeed valid Gauge Transformations?
I'm working my way through Griffith's Introduction to Electrodynamics. In Ch. 10, gauge transformations are introduced. The author shows that, given any magnetic potential $\textbf{A}_0$ and electric ...
- 103
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
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
$$ A_\mu (x_\mu) \to A'_\mu \equiv A_\mu (x_\mu) + ...
- 10.1k
6
votes
2
answers
5k
views
Landau level degeneracy in symmetry gauge, finite system
As we know, Landau level degeneracy in a finite rectangular system is $\Phi/\Phi_0$, where $\Phi=BS$ is the total magnetic flux and $\Phi_0=h/q$ is the flux quanta. This can be easily derived using ...
- 6,095
5
votes
1
answer
1k
views
$R_\xi$ gauges and the EM-field
$R_\xi$-gauges are said to be a generalization of the Lorenz gauge. I dont quite get why we add the term
$$
\mathcal L_{GF} = - \frac{(\partial_\mu A ^\mu)^2}{2\xi}\tag{1}
$$
to the Lagrangian. If i ...
- 2,196
2
votes
1
answer
2k
views
Gauge theory in classical electromagnetism
I understand gauge theory as the theory of continuous transformation group which keeps Lagrangian (or dynamics) invariant. So some integral invariants could be found. In terms of classical ...
- 458
2
votes
1
answer
1k
views
Why is the electromagnetic four-potential $A_{\mu}$ not an observable?
Why within classical field-theory the electromagnetic four-potential (usually $A_{\mu}$) not an observable?
In classical mechanics we don't have problems with energy measurements and in quantum ...
- 839
1
vote
2
answers
286
views
Coulomb Gauge misunderstanding
If we have $\vec A(\vec r,t)$ and $\phi (\vec r,t)$ and we make the following gauge transformations:
$$\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
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
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:
$$\nabla^2\phi+\frac{\partial}{\partial t}(\nabla\cdot \mathbf{A} )=0$$
$$\nabla^2 \mathbf{A} -\frac{\partial^2 \...
user153663
9
votes
2
answers
884
views
Why the extra term $\frac{1}{2}(\partial_{\rho}A^{\rho})^2$ in the photon Lagrangian?
In my quantum field theory class we have been told to use this Lagrangian for the photon field
$$\mathcal{L}=-\frac{1}{4}F_{\alpha\beta}F^{\alpha\beta}
-\frac{1}{2}(\partial_{\rho}A^{\rho})^2.$$
but ...
- 6,067
6
votes
1
answer
1k
views
Why does Coulomb gauge condition $\partial_i A_i =0$ pick exactly one configuration from each gauge equivalence class?
There are infinitely many configurations of a vector field $A_\mu$ that describe the same physical situation. This is a result of our gauge freedom
$$ A_\mu (x_\mu) \to A'_\mu \equiv A_\mu (x_\mu) + \...
- 10.1k
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