Question

what math do you need to know in order to understand quantum field theory. i was told that in order to understand string theory you need: topology, complex analysis, applied analysis, abstract algebra, tensor calculus, complex diffusion differential equation, multivariable calculus. anything else i should know? do the QFT books teach you this math or are you expected to already know it? i realize it's about 6 months before i start on this subject but i want to know how much work i have to do first.

Answer 1

http://quantumfieldtheory.org/

Answer 2

thanks but not necessarily what i was looking for.

Answer 3

My experience of physics subjects at university is that you are expected to know and to be good at mathematics,
You might want to add Linear Algebra to that list

Answer 4

I would say vector calculus and differential equations, of course. Analysis might be helpful for Green's function ideas, and linear algebra to deal with all those wretched indices. The unique piece for modern field theory is probably group theory, and that's probably the only one with which you won't already have coped in nonrelativistic quantum mechanics, E & M, and special relativity classes.

If you only have 6 months, however, what I would is go get a strong classical mechanics textbook, like Goldstein, and study the abstract theory, e.g. of Lagrangians and Hamiltonians. You could also perhaps profitably review what you know of propagators in a good quantum mechanics textbook, e.g. take a look at Feynmann and Hibbs. I would worry less about the math per se than about good conceptual mastery of the underlying principles of mechanics, which tends to be lost when you are studying quantum mechanics, focussed as it tends to be on the spectroscopy of bound systems.

Answer 5

great advice, i really appreciate your input

Answer 6

I forgot to add one thing: if it's been a while since you did E & M, or you did it only at an undergraduate level, you might also take out your Jackson (J.D. Jackson, Classical Electrodynamics) and restudy the classical theory of fields. Again, the significant challenge of quantum field theory is not the "quantum" so much as the "field," because most people come to it straight from nonrelativistic quantum mechanics, which doesn't do much with fields, as a rule. Good luck.