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).