Upper-level Books for Theoretical Physics: Lie Group & Functional Analysis

[_DJ_british_?]

Hi everyone,

I'm a Physics student and I'm planning to go to grad school in theoretical physics (I'm still in my first year so things may change but oh well) My question is twofold:

1. Any good book on Lie group and its application to physics, for someone with no formal course in group theory (Something that could build group theory up to Lie theory would be perfect!)?

2. A book on functional analysis, with application to Fourier Analysis and Probability (preferably).

My background is : Complex Analysis at the level of Stein, Measure Theory at the level of Halmos, Differential geometry at the level of Docarmo and Manifold Theory at the level of Boothby.

 

[hitmeoff]

You might want to try "Introduction to Lie Algebras" by Erdmann and Wildon.

I have the book and I've begun going through it, and it seems pretty good so far. I can't yet say definitively whether is a good book or not, but as far as I know, its the only Lie Algebra book that I know of.

According to the author, all you should need to understand the book and get something out of it is a good understanding of Linear Algebra at the level of Friedberg, Axler, etc; he does review all relevant L.A. in the book though. From what I've gone through so far, I do think some exposure to rigorous math is needed, which you clearly have. I do have previous experience with group theory though, and group theory is very different from subjects like Analysis, Diff Geo, etc.

But I really think, the only necessary prereq is that you have some experience learning and doing rigorous math.

As far as a book that covers Lie Groups and Physics at the UG level, I am not quite sure what to recommend. So I got curious and found this: https://www.amazon.com/dp/0521884004/?tag=pfamazon01-20

Its gotten a couple of good reviews. Maybe I'll pick it up myself.