Comprehensive book on group theory for physicists?

Question

I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that covers "all" the basics, and then, in addition, talks about the specific subjects of group theory relevant to physicists, i.e. also some stuff on representations etc.

Is Wigner's text a good way to start? I guess it's a "classic", but I fear that its notation might be a bit outdated?
This post imported from StackExchange Physics at 2014-05-04 07:46 (UCT), posted by SE-user Lagerbaer

Comments

Do you really want general group theory? I.e. theory of abstract groups, multiplication tables, classification of finite groups (using Lagrange's, Fermat's, Sylow's theorems, etc.), theory of presentations, uses of groups in number theory, etc.? Because if you just want to use group theory in physics then in my experience you won't need anything besides representations. See this question of mine over at MO: mathoverflow.net/questions/56304/…

This post imported from StackExchange Physics at 2014-05-04 07:46 (UCT), posted by SE-user Marek

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Well, since I don't know too much about group theory, I therefore also don't exactly know what I want. Seems that representations is the thing to look for.

This post imported from StackExchange Physics at 2014-05-04 07:46 (UCT), posted by SE-user Lagerbaer

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Should this be CW? I guess not, but I wasn't sure if we should run it as a list question for book recommendations. There isn't just one correct book to use.

This post imported from StackExchange Physics at 2014-05-04 07:46 (UCT), posted by SE-user David Z

Answer 1

There is no good book aimed at physicists. Robert Hermann, Lie Groups for Physicists is worth reading, but you didn't want something only about Lie Groups. Gelfand, Graev, and Vilenkin, Les Distributions, vol. 5 or, in English, Generalized Functions, vol. 5 is good for Fourier analysis on a group closely related to the Lorentz group, but not aimed at physicists, but is eminently readable and has some mistakes which don't really matter. Representations of finite groups are covered in Boerner, Representations of Groups: With Special Consideration for the Needs of Modern Physics an old classic written for physicists. None of these books are good, but they are the best I can think of. Strichartz has written about harmonic analysis on the actual Lorentz group, perhaps it is worthwhile, perhaps I will look at it some day...

A famous mathematician once told me no one had ever understood Weyl, The Classical Groups. I think much of it is covered by Boerner.

This post imported from StackExchange Physics at 2014-05-04 07:46 (UCT), posted by SE-user joseph f. johnson

Comments

I believe, although I can't find a reference, that when Dirac was once asked by a journalist whether there was anyone whose thinking was over Dirac's head, Dirac answered "Hermann Weyl".

This post imported from StackExchange Physics at 2014-05-04 07:46 (UCT), posted by SE-user WetSavannaAnimal aka Rod Vance

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The entire interview is included in the memorial volume edited by Kursunoglu and Wigner

This post imported from StackExchange Physics at 2014-05-04 07:46 (UCT), posted by SE-user joseph f. johnson

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arxiv.org/abs/0810.3328 Along with it study arxiv.org/abs/math-ph/0005032 . Life will be beautiful inshaallah.

This post imported from StackExchange Physics at 2014-05-04 07:46 (UCT), posted by SE-user Ome

Answer 2

"Lie Groups: An Introduction through Linear Groups" by Wulf Rossmann gets my vote. It gets the elementary ideas really cemented. Then read "Lie Groups, Lie Algebras, and Representations: An Elementary Introduction" by Brian Hall.

This post imported from StackExchange Physics at 2014-05-04 07:46 (UCT), posted by SE-user WetSavannaAnimal aka Rod Vance