Where to study "Group Theory Physics"?

[cuallito]

The field of physics I'm most interested in is group theory. I know it's technically a math subject, but I'm interested in using it in physics. So I guess you'd say "group theory applications in physics." I already have a Bachelor's in Engineering Physics from University of Oklahoma. I want to go for my PhD in this area. Should I be looking at physics or math programs? Any specific universities where this type of research is happening?

 

[homeomorphic]

I don't know a lot about the really deep applications of group theory (crystallography is one area), but if you are more interested in understanding the laws of nature than in doing math for math's sake, you should do physics, even if it means you end up not using much group theory. In math departments, there are only a few people who know physics well enough to have much more than a superficial relationship to real physics.

 

[bluechic92]

Look into theoretical particle physics.

 

[UVCatastrophe]

When it come to continuous symmetry operations, physics dominates in applications. I'd recommend checking out a book called An Introduction to Tensors and Group Theory for Physicists by N Jeevanjee.

However, group theory finds application in many other places. Here's a computer science problem that was solved with group theory techniques: http://users.cms.caltech.edu/~umans/papers/CKSU05.pdf

Look into theoretical particle physics.

Particle physics definitely has a huge variety of group theory applications. I wanted to add if you study any field of physics you will encounter group theory again.

I know some math guys that study group theory for physics applications (topological insulators) as well, but it's a different style of research. Different strokes for different folks

 

[Arsenic&Lace]

Now is a really dreadful time to be aiming at particle physics, the field seems to be continually shrinking. Condensed matter seems to involve some group theory if that's your cup of tea.

EDIT: That said you can find group theory applied practically anywhere but your mileage may vary. I saw a review paper a few months ago on applications of group theory to biophysics, which is not a subject anybody would expect to involve group theory.