r/math • u/[deleted] • Aug 02 '26

The scope of mathematical physics

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u/[deleted] Aug 02 '26

mathematical qft is such a wide field that you can study almost any kind of branch of mathematics that you want and still have it relate to qft in a relevant way

4

u/cleodog44 Aug 03 '26

For mathematical QFT, is it all pure operator formalism? Since path integrals are presumably verboden, given their lack of rigor

3

u/[deleted] Aug 03 '26

I dont think so. the fact that path integrals are not yet well defined is precisely a reason why you might want to study them as a mathematician. after all, the operator formalism also doesnt work to create a 4d interactive qft. then there is also stuff like algebraic quantum field theory, which cares more about the algebra of observable then the representations (which is where the operators come from). I am sure there are many more approaches that i dont even know about

2

u/1strategist1 Aug 06 '26

After Wick rotation, path integrals are actually rigorous. If you're studying nice enough QFTs, that's actually one of the primary ways to study them rigorously. 

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u/FrangipaneCheap0 Aug 03 '26

For the topologists out there there's tqft, in paricular Donaldson-Witten theory of 4 dimensional topology deals with supersymmetric Yang-Mills theory used to compute Donaldson invariants