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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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.
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.