What branch(es) of math are used in Quantum Field Theory?
Or the question, by way of analogy:
Tensor Calculus is to General Relativity as What is to Quantum Field Theory?
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$\begingroup$ Essentially a duplicate of physics.stackexchange.com/q/135104/2451 and links therein. $\endgroup$– Qmechanic ♦Nov 16, 2014 at 8:01
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First, caveat -- I am still in the learning phases of QFT.
Math skills used and needed:
Linear Algebra, vectors in Hilbert Space, Hamiltonians, Lagrangians (just like regular QM).
Tensor notation, 4-vectors, special relativity, metric tensors at times.
Feynman Path Integrals.
Calculus of Variations.
Fourier Analysis.
And, certainly this list is not complete due to my own level of understanding and not all the items above would be weighted the same.
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2$\begingroup$ "Feynman Path Integrals." That's not a field of math, per se, unless you're talking about measure theory on path spaces...I would also think "Functional Analysis" or "Operator Algebras" would prove useful... $\endgroup$ Nov 16, 2014 at 4:13
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2$\begingroup$ Group theory, especially Lie group and Lie algebra. $\endgroup$– SimonNov 16, 2014 at 4:31
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$\begingroup$ Thank you, hopefully someone more versed in the subject can outline the framework better. $\endgroup$– EriekNov 16, 2014 at 5:01
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$\begingroup$ I knew I forgot group theory right after I posted but I had a scheduled CW traffic net starting up and I could not miss that. $\endgroup$– K7PEHNov 16, 2014 at 5:29
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$\begingroup$ Calculus of variations is already used in classical mechanics (least action principle etc.). And Fourier analysis is already needed in regular QM (position to momentum space basis change). $\endgroup$– RuslanNov 16, 2014 at 6:23