Considering a switch to theoretical physics

[zpconn]

Considering a "switch" to theoretical physics

I'm a math major with 5 semesters left as an undergraduate. My math "profile" is very strong: lots of graduate classes (commutative algebra and algebraic geometry, homological algebra, higher homotopy theory and homology theory, representation theory and Lie groups/Lie algebras, etc.), research, etc. But I've recently come into contact with a new and unexpected temptress: theoretical physics. I'm considering shifting my education around now.

However, adding on a physics major is not so easy. I've transferred schools and have to make up a lot of general education requirements that unfortunately didn't come with me. In other words, adding on an entire physics major would cause me to take more time as an undergraduate than I want to.

I have two questions, and I would *really* appreciate any help anybody could offer.

(1) One possibility is for me to pursue my own physics education without getting an official degree (of course I will get a degree in mathematics). I'm talking about taking quite a few (no fewer than 10) graduate-level physics classes--general relativity, electromagnetism, mechanics, quantum mechanics (probably two semesters), quantum field theory, statistical mechanics, etc.

As you'll see in (2), I'm not sure I want to go to graduate school for physics specifically. But out of curiosity, how would this be perceived by physics graduate schools? I would be able to complete all the courses that, say, a Master's student would take for physics, and I would hopefully be able to do some research in the summer as well (though, as described in (2), not necessarily in ordinary physics). Does anybody have recommendations on how to best set-up my "customized" physics education?

(2) When I say theoretical physics, I really am focusing on the theoretical part. I love the beautiful interplay between deep mathematics and deep physics that is emerging today. I want to work in such an area, but I want the work to be mathematical--I don't want to do experiments. Could anyone offer some suggestions of areas to look at? I'd be especially interested in areas that aren't very well-researched (or perhaps have been heavily researched physically but not mathematically). As an example, I am somewhat familiar with the mathematical theory of quantum groups, but I have no idea about the corresponding physics. The mathematical theory is stunning. I'm sure that understanding both the mathematical and physical sides would be even more stunning. What would be a good path of education for me to gain a foothold in such an area?

To generalize: I'm trying to single out those areas of study which are simultaneously physics and mathematics, where the two fields each reduce to the other and coincide in unity. I would like to find the most beautiful of all such areas and rearrange my educational path so as to master it and start a research program in it when I get to graduate school. Just an example of what I have in mind that I found on the arxiv: http://arxiv.org/pdf/q-alg/9704002v2

With 5 semesters left, it seems like I should be completely capable of getting a foothold on the research in such an area. So I'm looking for advice on how best to do this. It seems such research is rare, and I don't know any faculty at my school who pursue it exclusively. There are definitely no classes on this material offered--the closest would be quantum field theory, which is on the physics side; but there's nothing on the mathematics side.

 

[MathematicalPhysicist]

I wonder how did you accomplish this with having 5 semesters left in your degree?

Are you somekind of a prodigy?

Anyhow if you got good grades on the advanced math courses, I don't see why they can't let you take already the advanced physics courses.

P.S
The courses you metioned are usually taken in the more advanced years of studies, even for undergraduates, so I wonder what will be left for you to take in your last 5 semesters?!

 

[Vanadium 50]

Let's back off a bit - how do you plan to take (and pass) graduate-level QM or graduate-level E&M without having had it at the undergraduate level?

 

[zpconn]

Let's back off a bit - how do you plan to take (and pass) graduate-level QM or graduate-level E&M without having had it at the undergraduate level?

You could be completely right, and it may not be possible or the prerequisites may be too great.

However, taking the example of electromagnetism, I have access to the course textbook (the one by Landau and Lifgarbagez) and doubt I'd have any trouble taking a class on the material. On the other hand, for quantum mechanics, I don't have access to the textbook, so I totally concede that I may be better off taking the undergraduate version, and of course I would do so if I realized that I don't have enough background for the graduate version. I'm currently abroad; otherwise I'd talk to someone at the physics department to get their thoughts.

My personal philosophy is it's best to take the most advanced classes I can handle--through experience I've found I learn a lot more this way--but I am absolutely willing to step back and take less advanced courses if the graduate versions turn out to be unsuitable for me.

I was also under the impression that graduate versions would focus more on the theory, which is what I want to learn, and less on problem-solving, which I'm less interested in--I realize I'm probably sending mixed messages about what exactly I'm interested in. I'm in a state of confusion about what I want to do with my life.

Basically, I don't know. I'm just throwing ideas around.

[As a side-note, I've taken some physics classes in the past--two years in high school, up through basic "plug-and-chug" E&M and special relativity. Probably the equivalent of just the standard two-semester course in general physics that most universities have.]

As for what I'm going to do the next 5 semesters, well, I'm trying to figure that out. The reality is I've discovered that I'm not as fond of things like commutative algebra as I thought I was.

 

[Vanadium 50]

I was also under the impression that graduate versions would focus more on the theory, which is what I want to learn, and less on problem-solving, which I'm less interested in--I realize I'm probably sending mixed messages about what exactly I'm interested in. I'm in a state of confusion about what I want to do with my life.

I would not characterize them thus. I would say that the problems tend to have fewer simplifying assumptions, and that they often require synthesis of different ideas (sometimes across courses) to solve them.