# Tagged Questions

A theorem that relates continuous symmetries (continuous transformations that don't affect the value of the lagrangian) to quantities conserved in time.

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### Hamiltonian mechanics and conservation of energy?

Can anyone explain to me Hamiltonian mechanics relation to conservation of energy? I'm not very good at mathematics, and I know it's important into understanding Hamiltonian mechanics. However, can ...
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### Help on understanding a concept in Noether's first theorem

Given a Lie group $G$, whose most general transform depends on $\rho$ parameters, under the action of which an integral $I$ is invariant, there are $\rho$ linearly independent combinations of the ...
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### Discrete translational invariance of lattice systems and conserved quantities [duplicate]

Imagine a crystal lattice with discrete translational symmetry. Is there any way to obtain local periodic conserved quantities by taking a derivative (deliberately left abstract)? The discretised ...
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### Lagrangians not related via a total time derivative lead to same Noether symmetries?

Having answered my initial two questions (v1), I now consider a third possibility. Consider two Lagrangians that both lead to equivalent equations of motion. Suppose that they are not related via a ...
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### Is there a systematic way to obtain all conserved quantities of a system?

I'd like to know whether, given a system, there's a way to obtain all the conserved quantities. For instance if the system consists of electric and magnetic fields, the fields must satisfy Maxwell's ...
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### Charge not conserved in scalar QED? [duplicate]

Since conservation of charge seems to be a well known concept, I am hoping that I am missing something and that the conclusion is incorrect. However, I have been unable to disprove this. Let me ...
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### Infinitesimal rotation of classical fields: why are rotation group representations important?

I understand that $SO(3)$ representations are important in quantum physics, because eigenspaces of the Hamiltonian are irreps of $SO(3)$ if it is part of the symmetry group. But I don't see the reason ...
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### 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 ...
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### Conservation Laws and time-reversal symmetry [duplicate]

In most dynamics books I've read they refer to conservation laws and their associated symmetries, cf. Noether's theorem. I know that the conservation of momentum is a result of the homogenity of ...