Research Orthogonal Lie Group for Physics Applications

[erbilsilik]

[Mentor's Note: Thread moved from homework forums]

Where can I start to research this question? I did not take any course on Group theory before and I know almost nothing about the relationship with this pure maths and physics. I've decided to start with Arfken's book but I'm not sure.


1. Homework Statement
Orthogonal Lie Group and the application of this group in physics

Homework Equations

The Attempt at a Solution

http://www.staff.science.uu.nl/~hooft101/lectures/lieg07.pdf

 

[Dr Transport]

WuKi Tung's book is a good place to start from a physics stand point, but without a background in group theoretical methods, it will be a tough read.

 

[strangerep]

Where can I start to research this question? I did not take any course on Group theory before and I know almost nothing about the relationship with this pure maths and physics.

I found Greiner's book on "QM -- Symmetries" quite helpful for acquiring an understanding of the (basic) math in the context of quantum theory. Of course, orthogonal groups are also relevant in relativity and elsewhere, but Greiner's book will get you started. (I found Greiner's series of textbooks especially good for introductory-level self-study since he doesn't skip steps.)

 

[erbilsilik]

So are you saying that I need to study the first 50 page in Greiner's book? I don't have a much time actually, looking for the best recipe for an answer 'one application of ortogonal Lie group in physics'.

 

[strangerep]

Well, when you said you wanted to "research this question", I thought you meant you wanted to acquire an understanding of the use of Lie groups in physics.

If you just want a "best recipe for an answer 'one application of orthogonal Lie group in physics', I could answer: "conservation of angular momentum", which is discussed in any respectable textbook on Classical Mechanics. But I daresay that would just lead to more questions.

You'll need to study a lot more than 50 pages, and from multiple textbooks, if you want to understand how to work with a Lie group. I only mentioned Greiner's book precisely because he got me over the basics in a reasonable amount of time. But yes, you'll have to actually read something, even if it takes a while.