How are symmetries defined mathematically?

Asked Mar 11 '14 at 17:14

Active Mar 11 '14 at 19:31

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I have started working on differential geometry very recently. I am little bit familiar with mathematical concepts such as manifolds, differential forms and associated concepts. As I was speeding through I caught interest in Lie groups and whose invaluable connection with the symmetries. I would be happy if anybody answers to these few questions.

I want to know what is a symmetry from the mathematical point of view?
How are $su2$, $su3$, and other symmetries first formulated?
What was the motivation?
How do we identify internal symmetries and corresponding conserved physical quantities?

edited Mar 11 '14 at 19:31

Qmechanic

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asked Mar 11 '14 at 17:14

cosmicman

Have you read much about Noether's theorem? – Kyle Kanos Mar 11 '14 at 18:22
I haven't worked out the theorem yet but I understand what it says. – cosmicman Mar 12 '14 at 14:20

How are symmetries defined mathematically?

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