Transitioning from Math to Physics

Question

I'm currently a 3rd year Math student and currently have one more year till I finish. Currently loving the degree, no problems.

But I'm really running into a giant problem. I fell in love with Physics recently after trying out Upper level Classical mechanics and Quantum Mechanics, and after much reading I realized it's indeed the field I'm more interested it.

Keep in mind I like pure math, I'm doing well in my courses and enjoying every second. But it's more so that I like learning math, than actually discovering/inventing new mathematical theorems pertaining solely to pure mathematical systems. But lately I've been enjoying Physics so much more, and strongly feel like it's where I belong.

My math knowledge: I took Real Analysis 1&2, Topology, Compelx Analysis, Measure Theory, Abstract Algebra 1&2, Number theory, Linear Algebra 1&2, Set Theory and lots of other Applied Math courses such as Math Methods, Numerical Analysis 1&2, ODEs and PDEs, and Stats/Prob courses like Probability Theory, Mathematical Statistics, and Statistical Methods. I enjoy all these courses, but I'd feel much more fulfilled if I can apply this knowledge to solve problems in physics than just doing math for the sake of math.

Now unfortunately I cant do a double major (not a thing in my country). Is there a way I'd get accepted to theoretical physics PhD programs by finishing my math degree, studying the necessary physics alone (I'm on good terms with both the Math and Physics faculty so they could certainly vouch for my knowledge, if I manage to reach an appropriate level and prove myself to them) and maybe do the Physics GRE? How much would it affect me if I have no Physics resesech experience (I do have Math research experience with my professors)?

Or should I do a physics undergrad and do research with my professors?

Thank you very much for any advice, and sorry if I said something that might seem bad, offensive or ignorant.

P.S: I should mention now that a masters in Physics in my country is impossible unless I do a bachelors all over again (abroad is a different story).

Answer 1

First and foremost, there exist physics-related projects on which you can work while being a PhD student at a mathematics department. Here is one example out of many.

Also, both in the US and Europe, with you Math degree you can apply to many PhD programmes in physics or engineering. (If admitted, you will have to take some remedial courses.) Moreover, in some areas, your mathematical background will sooner be an advantage. One example of the kind is furnished by celestial and orbital mechanics or control engineering. Another is QFT, superstrings, quantum gravity (and gravitational physics in general).

Answer 2

This will probably have a different answer in a different country, but for doctoral study in the US, you would probably be considered for admission. It is common here to change fields on start of a doctoral program. There will be advanced physics courses to take, however.

The competition is fierce, however, and you will be competing with others who have had more physics.

But another degree, or changing as an undergrad, isn't required. Letters of recommendation from people who can honestly predict success in physics would be very important.