Applications of Algebra in Physics

Often I have heard about the link between Algebra (in particular Representations of Groups and Algebras) and some “indefinite” field of Physics.

I have a good preparation in Algebra and Representation Theory (in particular about Representations of Lie Algebras), and I’m fascinated with Physics. My idea is try to understand this link and eventually study it with more depth.

Hence I’m looking for an introductory book that emphasizes the applications of Algebra in Physics from a comprehensible and mathematical point of view.

Does anyone have an idea for a book with these requisites?

Thank you!

Solutions Collecting From Web of "Applications of Algebra in Physics"

Howard Georgi’s “Lie Algebras in Particle Physics” is good, if more intended for the physicist going towards the math than vice versa. It should provide a lot of context, though, and there’s a PDF version floating around on google. I’d say similar things about these two introductions to aspects of high-energy theory [1] [2].

I’ll see if I can remember some other good ones.

Peter Woit, the author of the book “Not Even Wrong” and a blog by the same name, has been working on a book on quantum mechanics as described by representation theory. The latest draft may be found at the following link:

Quantum Theory, Groups and Representations:
An Introduction.