Giving an action, a general one:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]S = \int dt L(q^i,\dot{q}^i,t)[/tex]

now assume this action is invariant under a coordinate transformation:

[tex]q^i \rightarrow q^i + \epsilon ^a (T_a)^i_jq^j[/tex]

Where T_a is a generator of a matrix Lie group.

Now one should be able to find the consvered quantities, the "Noether Charges", and how those relate to the matrix lie group.

BUT HOW?

I have never done so much in school about actions, just lagrangians and hamolitonians.

For instance, if one only considered translation: [tex]q^i \rightarrow q^i + \epsilon q^i[/tex], and if the Lagrangian/hamiltonian is invariant under translations -> we know that the linear momentum is conserved. But how do we show it with the action and noether currents/charges?

Now this is a quite general question, I have never quite understood this, and is related to what I asked a couple of days ago in the math section about Lie Subgroups. I am trying to appreciate Group Theory, in perticular Lie Groups. This is a "general example" on its application to classical mechanics which I found somewhere, but then I found out that I am totally lost when it comes to performing the "searches" for noether charges.

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# Homework Help: Finding Noether Charges from Action

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