Can one do mathematical physics and theoretical physics at the same time?

[Jamestein Newton]

I finished my 1st-year physics, took analysis, linear algebra, mathematical logic, classical mechanics, quantum mechanics(I was exempted from intro phy and took some 3rd-year physics courses)

I internal transferred to pure maths. The reason is that the curriculum of the physics programme in our school is not suitable for applying to the theoretical physics programme(no qft, advanced gr). Also, no one does purely theoretical physics in my school but there are people doing computational and phenomenological theoretical physics but that's not my interest.

Instead, our school has a strong math department and there are many people doing math-ph.

For now, I get along well with one of the profs doing geometric analysis. He knew nothing about GR but he hold a reading course on GR with one student. Then the student taught him back a lot of GR and thus he was recommended by that prof to Princeton to do mathematical GR research.

According to the supervisors I found in my department who matches my research interest, the possible undergraduate research I can do are
(1)beyond GR, some qc-gr
(2)quantum groups
(3)quantum information theory

Indeed they are math-ph. I know very well the difference between mathematical and theoretical physics. I am fond of theoretical physics more and I also love mathematical physics. I found mathematical physics is like manipulating maths underlying or on the surface to develop the mathematics(?)The maths prof will become my supervisor means that I will play an active role during the research. Is it possible to bring the math-ph research with some theoretical physics taste, merging them together? Can one achieve such a balance?

That's what I was referring on the title "Can one do mathematical physics and theoretical physics at the same time?"

 

[Jamestein Newton]

The new situation for me is that I am not a 100% pure maths student.

In my plan, if I take one more course, I get the physics and cosmology double minor.
Only if I take two more experimental physics courses(which I prefer not to do but it depends on my future progress), I get a second major in physics

 

[Frabjous]

What books did you use for classical and quantum mechanics and what were your grades? What about electrodynamics?

 

[Jamestein Newton]

What books did you use for classical and quantum mechanics and what were your grades? What about electrodynamics

What I mentioned is indeed the courses I have official records of.

I have taught myself electrodynamics(Griffiths) and thermo & stat mech(Schroeder

Classical mechanics(Marion, Goldstein, Landau)
QM(Shankar)

In my 2nd-year I will take smooth manifolds+riemannian geometry (year-long sequence both uses john m lee's textbook). I would also take a GR course that uses Wald's text, studying some exact solutions and global structures in GR. That's an 1on1 study course with math prof

I have CGPA 3.7+. Poor grades in general education courses however I took a lot of courses(overload) so my CGPA becomes better. All the maths and phys course are A grade

 

[romsofia]

Yes, and no.
If you're asking if, you, the student can do both at once? Of course, it's just abstract lines we draw to differentiate the fields. Study whatever you want in your free time.

The no comes from doing both on a research stint. I would be lying if I never envisioned myself doing it all when i was younger. I'd not only sketch out some theoretical solutions, but I'd also justify it rigorously mathematically! Then, reality hits, and timelines are a thing. So I'd never recommend doing both full heartily on one project, because you may just end up getting nothing substantial done in a time frame.

 

[Frabjous]

You need to worry about developing gaps in your knowledge. That being said, A’s and graduate level courses as a sophomore demonstrate potential. So I would say yes. I agree with @romsofia and would say that too much research as an undergraduate can be risky. You are charting an independent course so you need to be working with the academic advisors in both the math and physics departments; they know you better than anyone at PF.

 

[Jamestein Newton]

Yes, and no.
If you're asking if, you, the student can do both at once? Of course, it's just abstract lines we draw to differentiate the fields. Study whatever you want in your free time.

The no comes from doing both on a research stint. I would be lying if I never envisioned myself doing it all when i was younger. I'd not only sketch out some theoretical solutions, but I'd also justify it rigorously mathematically! Then, reality hits, and timelines are a thing. So I'd never recommend doing both full heartily on one project, because you may just end up getting nothing substantial done in a time frame.

What I want to do is that I want to build my special taste. I see concerns between researchers working in math-ph and theoretical physics, and it would be fun if I can communicate with researchers working in those two styles, and me going forth between those two disciplines.

 

[Jamestein Newton]

so you need to be working with the academic advisors in both the math and physics departments; they know you better than anyone at PF.

Yeah. I wouldn't really take the opinions form internet forums seriously(or weigh them less), but I am always looking for a random discussion for fun.

 

[romsofia]

What I want to do is that I want to build my special taste.

Yes, but you have to start with one, and complete a project within a time frame. You have to understand, to stay in academia, you have to produce some work. Before you can develop that "special taste" you have to showcase you have a tongue that can taste to begin with. In other words, while you pursue your first specialty, make sure to read papers in other journals.

Think of some cross research, but at these early stages, you're most likely not going to have time to do both, and if you go in with the expectation that you'll be able to pursue both, you're either going to burn out, or put out mediocre papers that no one really cares about.

A lot of people drop out of doctoral programs due to burn out, and it would suck if someone with your passion does the same. Go in with reasonable expectations (that is, you'll only be able to pursue one), and you're less likely to be another statistic.

I see concerns between researchers working in math-ph and theoretical physics, and it would be fun if I can communicate with researchers working in those two styles, and me going forth between those two disciplines.

A fun paper on this topic can be found in the book: "Quantum theory of gravity. Essays in honor of the 60th birthday of Bryce S. DeWitt" titled "What have we learned from quantum field theory in curved space-time" by Fulling. If you can get access to this paper, you'd enjoy it. But remember, ultimately, it takes a long research career to be able to branch out.