How much mathematics do I need to know to start Quantum Field Theory?

[HakimFaizaan]

I plan to study from Peskin and Schroeders book if it helps, I just need to know what topics I need to study and it would be greatly appreciated if someone could tell me what books are good on the subject, I have a limited budget however and if I could get a single or only 2 or 3 books covering all the material it would help a lot.

 

[bapowell]

I plan to study from Peskin and Schroeders book if it helps, I just need to know what topics I need to study and it would be greatly appreciated if someone could tell me what books are good on the subject, I have a limited budget however and if I could get a single or only 2 or 3 books covering all the material it would help a lot.

That depends on your current level of mathematical knowledge. Off the top of my head, the Peskin and Schroeder treatment makes use of (and these are more keywords than subject areas): techniques from complex analysis (like contour integration), Fourier transforms, and Green's functions for the introductory material. You'll need some group theory to understand symmetries in particle physics. A base understanding of calculus up through differential equations, and linear algebra, is assumed.

 

[The_Duck]

You need to have a solid understanding of quantum mechanics and classical electrodynamics. If you've done these, then you have most of the mathematical prerequisites. I think the one main thing you may not have seen before is contour integration. You don't really need a textbook just for that; you can Google up plenty of information. bapowell mentions group theory, but QFT textbooks, including P&S, generally include an introduction to the group theory you need, so I don't think you necessarily need to study that separately.

 

[HakimFaizaan]

So I don't need to study topology?

 

[bapowell]

So I don't need to study topology?

No, not for the fundamentals. There are certain topics in field theory that require it, like the Bohm-Aharanov effect, but these are ancillary.