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What?!??? Physics is chock full of symmetries, and group theory was developed to address exactly this stuff!!! Gee...I would tell you to take a course in group theory!
It's never too late...& I "profited" from studying group theory. Actually, I wish I had known more about it in undergrad math level; only formally took it in my grad years. Fast advice for physics-minded: study both finite and topological groups...both are used a lot in physics!
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