Can anyone expand on the relationship between Lie groups, Lie algebras, exponential maps and unitary operators in QM? I've been reading lately about Lie groups and exponential maps, and now I'm trying to tie it all together relating it back to QM. I guess I'm trying to make sense of how Lie groups emerge in QM, and also how the physics approach to Lie groups (that I've seen so far, at least) tends to emphasize the fact that a subset of the Lie group in the neighborhood of the identity can generate the entire group (rather than thinking about Lie groups strictly as groups endowed with a C^infinity manifold). I'm not totally sure why all this becomes so relevant in QM - anyone care to comment? :)(adsbygoogle = window.adsbygoogle || []).push({});

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# Lie groups in QM

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