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First Impressions Book Review: Lie Groups for Pedestrians.
blaisepascal
First impression: Apparently I need to find the book "Lie Groups for Crawlers" first.

Lie groups (pronounced "Lee", after Sophus Lie, the Norwegian mathematician who developed the theory) are somewhat central to a certain level of understanding of modern physics. Mathematically, groups in general describe symmetries, and "continuous groups" (another term for Lie groups) describe continuous symmetries. The symmetries, in turn describe structure. Saying that a mathematical construct or set of equations has a particular group structure allows you to infer stuff about the mathematical construct or set of equations.

Mathematical physicists like Emmy Noether discovered that symmetries of physical laws imply conservation laws. Because physical laws have a time-translation symmetry (e.g., the same laws apply now as last week) energy is conserved. Because they have a space-translation symmetry (the same laws apply here as there) momentum is conserved. And so forth. So identifying what symmetries, what group structure, holds for various physical laws are important to understanding the laws.

That's why I'm interested in group theory, and since Lie Groups seem to be prominent in quantum physics, I'm interested in Lie Groups. And that's why I recently bought two.

"Lie Groups for Pedestrians" was written in the mid 1960's as a book for introducing physicists to Lie Groups. As such, it assumes the mathematical acumen of a trained physicist from the mid 1960's who might not be familiar with Lie groups. As such, it doesn't start slow. It begins with a review of quantum spin operators and the important commutators among them. If you don't know what that means, you are only a little ways behind me. It is disconcerting, to say the least, when the first example in the introduction is pushing your limits.

It didn't take me long to put it down to check out the second book I bought on the subject.

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So when does the movie come out?

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