I'm looking for someone to talk to about mathematical physics

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Hi everyone! My name is Vitaly, and I’m a third-year student at MIPT (Moscow Institute of Physics and Technology), studying at the Faculty of General and Applied Physics, in the department of Mathematical Methods of Modern Physics, which is headed by Roman Nikolaevich Karasev.

I truly became passionate about physics back in the 8th grade, when I completed two online courses by A. S. Chirtsov — one on kinematics and another on celestial mechanics. That’s where I first encountered the ideas of Special and General Relativity, as well as the grand challenge of modern theoretical physics that Einstein formulated after developing General Relativity: the creation of a unified field theory that would combine all four fundamental interactions — electromagnetic, strong, weak, and gravitational. That was the moment I realized I wanted to dedicate my life to solving this problem.

Later, I enrolled at MIPT, in the FOPF (Faculty of General and Applied Physics). But I was soon disappointed by how physics is taught here. All the physicists I’ve met at my university seem to have a dismissive attitude toward mathematics. The math courses offered to theoretical physics students are extremely simplified, often skipping proofs entirely — they’re mostly just about applying techniques to solve particular equations. Almost every theoretical physicist I’ve come across here views mathematics merely as a tool, and they believe that digging too deep into it will only distract from real discovery.

But I completely disagree. I believe that mathematics has always been the true source of the greatest breakthroughs in physics. For instance, the principle of least action may have once seemed like a purely mathematical curiosity — after all, classical mechanics worked just fine in Newton’s formulation. Yet today, this principle is foundational to all of theoretical physics. Likewise, without differential geometry, General Relativity couldn’t have been created at all.

That’s why I chose to join the math department instead of a physics one. However, I quickly realized that even in my department, no one seems to be familiar with the kind of mathematics I’m truly interested in. For example, I started reading Quantum Mechanics for Mathematicians by Takhtajan, and came across a concept I had never heard of — Frechet manifolds. To my surprise, no one at my university had even heard of them, and I wasn’t able to find any literature that clearly explains what they are.

I’m hoping that here I’ll be able to find people who share my views — people I can discuss books with by authors like Takhtajan, Faddeev & Yakubovsky, and Sardanashvili, and who can help me find my way forward.
 
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Vyurok said:
Sardanashvili

Oh, I met him at one of the "geometry in physics" conferences. I guess you're interested in the things that I was interested in when I was 'actively' doing physics at Warsaw University. What drew me into geoemetry was the idea of "Tluczyjew triples" - morphisms between duble vector (or affine-vector in field theory) bundles that united Lagrangian and Hamiltonian "sides" of mechanics and field theory smoothly. More smoothly than anything else, in my opinion. Paweł Grabowski, along with his wife Katarzyna, and Paweł Urbański, are 'main characters' doing reasearch on that at Warsaw Uni. Ah, good old times.

Anyways, welcome to PF!
 
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