Linked Questions
16 questions linked to/from Classical EM: clear link between gauge symmetry and charge conservation
182
votes
5
answers
25k
views
Gauge symmetry is not a symmetry?
I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
- 17.1k
75
votes
5
answers
11k
views
Is the converse of Noether's first theorem true: Every conservation law has a symmetry?
Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law.
Is the converse true: Any conservation law of a physical ...
- 5,318
52
votes
5
answers
16k
views
Noether charge of local symmetries
If our Lagrangian is invariant under a local symmetry, then, by simply restricting our local symmetry to the case in which the transformation is constant over space-time, we obtain a global symmetry, ...
- 8,540
42
votes
4
answers
12k
views
Noether's theorem and gauge symmetry
I'm confused about Noether's theorem applied to gauge symmetry. Say we have
$$\mathcal L=-\frac14F_{ab}F^{ab}.$$
Then it's invariant under
$A_a\rightarrow A_a+\partial_a\Lambda.$
But can I say that ...
- 701
30
votes
3
answers
9k
views
Physical difference between gauge symmetries and global symmetries
There are plenty of well-answered questions on Physics SE about the mathematical differences between gauge symmetries and global symmetries, such as this question. However I would like to understand ...
- 1,336
22
votes
3
answers
13k
views
Noether theorem, gauge symmetry and conservation of charge
I'm trying to understand Noether's theorem, and it's application to gauge symmetry. Below what I've done so far.
First, the global gauge symmetry. I'm starting with the Lagragian
$$L_{1}=\partial^{\...
- 10.6k
26
votes
4
answers
6k
views
What is the symmetry which is responsible for preservation/conservation of electrical charges?
Another Noether's theorem question, this time about electrical charge.
According to Noether's theorem, all conservation laws originate from invariance of a system to shifts in a certain space. For ...
- 2,080
20
votes
1
answer
9k
views
Noether's first theorem and classical proof of electric charge conservation
How to prove conservation of electric charge using Noether's first theorem according to classical (non-quantum) mechanics?
I know the proof based on using Klein–Gordon field, but that derivation use ...
user8817
3
votes
2
answers
202
views
Is gauge symmetry necessary for charge conservation?
The common view is that gauge symmetry is necessary for conservation of charge(s) in Yang-Mills theory. But one thing I have never been able to get out of my head is, if there isn't any other possible ...
- 7,504
0
votes
0
answers
796
views
Meaning of the Noether current on a global $U(1)$ gauge transformation
Using the gauge principle we can derive the QED lagrangian from the dirac lagrangian,
$$
\mathcal{L}_{Dirac}=\bar{\Psi}(i\gamma^{\mu} \partial_{\mu}-m\hat{I})\Psi
$$
$$
\mathcal{L}_{QED}=\bar{\...
- 157
1
vote
0
answers
699
views
From gauge invariance to charge conservation in covariant electrodynamics
I tried to solve the equations of motion using the action for the electromagnetic field interacting with a current, like
$$ L = F_{\mu\nu}F^{\mu\nu} + A_{\nu}j^{\nu} $$
getting the right Maxwell's ...
user71714
5
votes
1
answer
330
views
Noether Charge and Gauge Fields
I understand the global gauge symmetry results conserved charges associated with the symmetry. My question is, why don't we have conserved charges associated with local gauge symmetry of the gauge ...
- 1,080
0
votes
0
answers
689
views
Noether current and continuity equation in classical scalar QED
Consider the following scalar QED model
\begin{align}
S = \int \mathrm{d}^{d+1} x\,
\left\{-\left(\mathrm{D}_{\mu}\phi\right)^{\dagger}
\left(\mathrm{D}^{\mu}\phi\right)
-m^2 \phi^{\dagger}\phi - \...
- 1
0
votes
1
answer
387
views
Electric Current in Classical Electrodynamics derived as Noether current [duplicate]
I'm looking for a derivation of the often quoted fact that
the conservation of electric(!) current $j^{\mu} = (c \rho, \vec{j})$ in
relativistic classical electrodynamics is an explicit consequence of
...
- 1,395
0
votes
0
answers
354
views
Applying Noether's Theorem to local invariance
I have realised that I am unsure about how I can apply Noether's theorem to a Lagrangian with local invariance. For instance, the following Lagrangian has a local $U(1)$ invariance:
$$\mathcal{L}=(D_{...
- 1,224