All Questions
Tagged with degrees-of-freedom gauge
17
questions
19
votes
2
answers
2k
views
Gauge-fixing of an arbitrary field: off-shell & on-shell degrees of freedom
How to count the number of degrees of freedom of an arbitrary field (vector or tensor)? In other words, what is the mathematical procedure of gauge fixing?
- 291
18
votes
1
answer
4k
views
Gauge fixing and degrees of freedom
Today, my friend (@Will) posed a very intriguing question -
Consider a complex scalar field theory with a $U(1)$ gauge field $(A_\mu, \phi, \phi^*)$. The idea of gauge freedom is that two solutions ...
- 26.6k
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
10
votes
2
answers
2k
views
Counting massive degrees of freedom after gauge fixing
Consider the theory of scalar QED with the Lagrangian
$$\mathcal{L} = - \frac14 F^{\mu\nu} F_{\mu\nu} + (D^\mu \phi)^* (D_\mu \phi) - m^2 \phi^* \phi \tag{1}$$
where $\phi$ is a complex scalar field ...
- 103k
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:
$$\nabla^2\phi+\frac{\partial}{\partial t}(\nabla\cdot \mathbf{A} )=0$$
$$\nabla^2 \mathbf{A} -\frac{\partial^2 \...
user153663
9
votes
2
answers
2k
views
How many degrees of freedom in a massless $2$-form field?
Consider the Kalb-Ramond field $B_{\mu\nu}$ which is basically a massless $2$-form field with the Lagrangian
$$
\mathcal L = \frac{1}{2}P_{\alpha\mu\nu}P^{\alpha\mu\nu}\,,
$$
where $P_{\alpha\mu\nu} \...
- 2,568
2
votes
2
answers
207
views
"One-parameter" gauge transformation
In my advanced classical physics course, it was stated that the electromagnetic field strength tensor $F_{\mu\nu} = \partial_{\nu}A_{\mu} - \partial_{\mu}A_{\nu}$ is invariant under "one-...
- 234
2
votes
1
answer
2k
views
Residual Gauge Freedom [closed]
How are we still left with one Residual Gauge Freedom in the choice of Electromagnetic Potential after having already exploited the Gauge Freedom once.
As is mentioned in Halzen and Martin Section 6.9....
- 169
2
votes
1
answer
575
views
Coulomb gauge and two degrees of freedom of EM field
The EM field has two possible polarizations, which is caused by spin-one nature of field (leads to the Lorenz gauge) and massless of the field. Really, the Klein-Gordon equations for the EM field
$$
\...
user8817
2
votes
0
answers
56
views
$R_\xi$ gauge and degrees of freedom counting
In the standard classical Maxwell theory, we use the following arguments to claim that there are only two propagating degrees of freedom
$A_\mu$ has 4 components
$A_0$ is non-dynamical (-1)
$\...
- 669
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
1
vote
1
answer
102
views
Counting degrees of freedom without fixing the gauge?
In electrodynamics, the current-current interaction in the momentum space is described by
$$p^2 A_\mu J^\mu = J_\mu J^\mu \, ,$$
where $J$ denotes an arbitrary external current. Since photon-...
user20250
1
vote
0
answers
53
views
Counting degrees of freedom in theories with two-forms [duplicate]
I am reading Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics. I am thinking that I can apply the same arguments to the case of a two form, whose components are ...
- 3,992
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