# Questions tagged [symmetry]

We say that something is symmetric if there is some transformation we can perform on that object that leaves some property unchanged. The set of symmetry transformations of an object form a group, and the name of this group is used as the name of the symmetry of the object.

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### Comparison between formulations of Noether's theorem

Version 1: An infinitesimal variation on the fields $\phi\mapsto\phi'$ is said to be a symmetry if $\delta \mathcal{L}:=\mathcal{L}(\phi',\partial\phi')-\mathcal{L}(\phi,\partial\phi)$ is a total ...
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### Solving Many DOF System with Symmetry (Eigenvector issue)

I'm working on dealing with the simple harmonic oscillations of a benzene atom. We're meant to solve it with symmetry. I can solve it by going the longer way via the Euler-Lagrange method and finding ...
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### How can the position operator be displacement invariant?

I am reading chapter 3 of Quantum Mechanics - A Modern Development by Leslie E Ballentine, where he derives the operators for the common dynamical variables from space-time symmetry considerations. At ...
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### Time-independent source and quantum field theory

Can anyone explain the fundamental reason of why time-independent sources cannot emit or absorb energy. Does it have to do with time-translation symmetry and Noether's theorem? I was studying the ...
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### BETRANDS THEOREM [duplicate]

For a force that behaves like $$F=k r^n,$$ the stability condition requires $n > -3$. How this leads to the Bertrand’s theorem: The only central forces that result in closed orbits for all bound ...
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### Symmetry group in physics [closed]

When we say like “spatial translation/rotation” symmetry in physics context, do we really mean the representation of the symmetry group in coordinate basis rather than the “symmetry group” itself?