All Questions
Tagged with degrees-of-freedom gauge
8
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
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
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
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
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
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
0
votes
1
answer
2k
views
General relativity: gauge fixing
In his lectures professor Hamber said that the metric tensor is not unique, just like the 4 vector potential is not unique for a unique field in electrodynamics. Since the metric tensor is symmetric, ...
- 1,068