While i'm talking books, is there a Fields, Sets and Algebras for Dummies

[davelee]

While I'm talking books, is there a "Fields, Sets and Algebras for Dummies"

Where dummies = physicists (me!). I've been baffled thus far by statements such as "SU(2) is a representation of such and such in R^2" and similar statements made in reference to the standard model and isospin. I fail to appreciate the significance probably since I have not ever studied real analysis and fields from a "math" perspective. However, is there a way I could read up on this without being forced to begin with a proof of constructing real numbers from the rational numbers, while still getting the essential properties of fields, etc., and the lingo to go along with it?

 

[selfAdjoint]

The representation of SU(2) etc. fall into the area of Lie groups and their Lie algebras. (I have to insist that Lie, a man's name, is pronounced LEE!) There are three levels of learning.

1) Learn the basic groups used in physics (SU(2), SU(3), SO(1,3), and maybe S2(L,C), SU(N), and SO(N). Only specialists need E8. The popular representations are described in the introductory sections of quantum field theory texts, including Ryder and Kaku. Memorize them and you can understand most of what's going on in the standard model.

2) Learn how to build representations yourself for these and closely related groups. You might want to do this if you plan on writing research papers in field or stringy physics. There are specialized texts for this, although the Dover book Group Theory and its Application to Physical Problems by Hammermesch, is a pretty good intorduction, in which you can skip a lot of stuff.

3) Get hung up on the full bore mathematical theory of representations. There are mathematicians right now working on the the represention theory of infinite dimensional things you never heard of and will probably (but not certainly!) never need in physics.