All Questions
Tagged with degrees-of-freedom gauge
17
questions
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answers
60
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Degree of freedom - Lorentz transfomation reduces it? [duplicate]
I am having a real difficult to counting degree of freedom. In fact, I notice that sometimes I am confused about what exactly we count as DoF, and what we do not count.
See, for example, the ...
- 980
1
vote
0
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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 ...
- 3,982
2
votes
0
answers
56
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$R_\xi$ 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
2
votes
2
answers
207
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"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
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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
9
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2
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2k
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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
1
vote
3
answers
378
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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
10
votes
2
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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
1
vote
1
answer
102
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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
10
votes
1
answer
3k
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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
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2
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2k
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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
2
votes
1
answer
2k
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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
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1
answer
2k
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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
18
votes
2
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3k
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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 ...
- 6,361
19
votes
2
answers
2k
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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?
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