Learning Point Group Theory: Challenges of Lee Groups

[zwoodrow]

Hi Everyone,
Back in college i informally learned what i would call point group theory. Most of it never touched on continuous transformations. When I learned it back then it was all pretty straight forward. Recently I have been trying to learn about Lee groups (to understand symmetries in Lagrangians in field theory), however whenever I pick up a book or tutorial its like hitting a wall- it doesn't seem like group theory at all. Does anyone have a good book or tutorial or video to recommend?
I appreciate any input.
thanks
doug

 

[bapowell]

It's actually spelled 'Lie Group'. Maybe that's why you couldn't find any good refs ;)?

One good reference is Georgi's "Lie Algebras in Particle Physics" -- obviously the treatment is developed towards particle theory, but the beginning chapters are generally helpful.

 

[zwoodrow]

thank you, oh dear god i am going to be crucified by all of the nerds for that one.

 

[bapowell]

Yeah, you know, I'd like to offer some words of encouragement, but they're going to destroy you

 

[Dickfore]

Because it's not the same guy as Bruce Lee, you know.

 

[nicksauce]

Schutz's "Geometrical Methods of Mathematical Physics" has a quite gentle introduction. I'd recommend it.

 

[DrDu]

Sternberg, "Group Theory and Physics". It's quite an unusual but very elegant book. He does not only treat Lie Groups but also point groups and permutation groups, from a very modern point of view.
However, there are loads of typos.

 

[MathematicalPhysicist]

Well I used a textbook by Brian Hall (search for his name and you'll find the textbook).

It's an easy going textbook with minimal prequisites, though I would recommend having taken a course in topology and knowledge of manifold theory to some extent.

All the beckground knowledge needed to read the bulk of the book is in the appendices.
My critic is partial cause I haven't read all through it, perhaps next year accompanied with a course can be a good start.

Cheers.

 

[atyy]

Lecture notes at http://webusers.physics.illinois.edu/~m-stone5/mmb/mmb.html