Symmetry Groups Algebras Commutators Conserved Quantities

friend

Symmetry, Groups, Algebras, Commutators, Conserved Quantities

OK, maybe this is asking too much, hopefully not.

I'm trying to understand the connection between all of these constructions. I wonder if a summary about these interrelationship can be given.

If I understand what I'm reading, there is a connection between finite groups and algebras, though I think I'm confused between what objects are involved in each and what each acts upon if anything. And I understand that there is a conserved quantity for every symmetry, but this is only for symmetries of Action integral, right? What I'm not sure about, though, is whether there is a connection between algebras and commutation relations. Any insight you could give in these areas would be appreciated. Thanks.

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friend

Re: Symmetry, Groups, Algebras, Commutators, Conserved Quantities

OK, maybe this is asking too much, hopefully not.

I'm trying to understand the connection between all of these constructions. I wonder if a summary about these interrelationship can be given.

If I understand what I'm reading, there is a connection between finite groups and algebras, though I think I'm confused between what objects are involved in each and what each acts upon if anything. And I understand that there is a conserved quantity for every symmetry, but this is only for symmetries of Action integral, right? What I'm not sure about, though, is whether there is a connection between algebras and commutation relations. Any insight you could give in these areas would be appreciated. Thanks.
For example, as I understand it, conserved quantities only apply to continuous symmetries of the Action integral. Or are there conserved quantities for finite symmetries as well?

I thought I heard people say that the commutation relations define the algebra, is this right?

Moderator: Do you think this thread should be moved to Quantum Physics Forum? That is what is motivating these questions.

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