What Should I Know Before Learning QFT?

[Saussy]

I have already done quantum mechanics (and general relativity if it is relevant) and have all the associated math prerequisites but not much more than that. Is there anything I should add before attempting QFT and what text would be best for these? In addition, what text would you recommend for QFT itself?
Thank you for any help.

 

[vanhees71]

Just start with QFT and fill math gaps when they appear. With a solid foundation in quantum mechanics and some basics in relativistic classical field theory (electrodynamics) you should be able to get a good start into QFT.

My farvorite books are the three volumes by Steven Weinberg, The Quantum Theory of Fields, Cam. University Press. They are, however very chalenging for the beginner, and that's why I recommend as a step before a more conventional textbook. For this purpose, I think Ryder, Quantum Field Theory is one of the best I know. Another very good book is Bailin, Love, Gauge Theories. It's more focused on the path-integral approach from the very beginning.

You might like to have also a look at Peskin/Schroeder's book, but I've to warn you that it contains a lot of sloppiness and even some mistakes/typos. Totally inacceptable is only Zee's, QFT in a Nutshell. It doesn't explain enough details for the beginner and is quite superficial all over.

 

[muppet]

First of all, this has been answered in the preface to Srednicki's QFT text, a draft of which is available free:
http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf
There he lists in the preface some equations that if you recognise all of them, then you should be able to follow everything in the book. (It's also a useful, and free, book!)

When you say you've "done" quantum mechanics... this needs to have been at a reasonably advanced level to really appreciate what's going on in field theory. For example, would you be comfortable explaining to someone what exactly the Pauli matrices have to do with spin-1/2 particles; what the S-matrix is; and what the relationship between unitary operators that depend continuously on some parameter (such as rotation by some angle ) and observables is, and how this parallels Noether's theorem from classical mechanics? If so, you should be fine.

The great thing about Weinberg's text is that he builds QFT out of familar quantum-mechanical principles, so that if you're not completely comfortable with e.g. the scattering formalism, he develops it for you in a way that suits the subsequent development. There's also all kinds of stuff in there that really can't be found anywhere else. The downside is that this makes it a bit of a slog. If you're not familiar with these ideas then learning them from Weinberg is hard going (as I found!), because it's really intended as a review from a particular vantage point. Furthermore, because of the unique logical structure of his book, as well as highly unconventional notation, it's essentially impossible to get around working through the book in detail. If you're studying on your own, then this obviously shouldn't be a problem, but if you're studying for a course then the development in Weinberg might be too slow for your reading to keep pace with lectures that adopt any other approach to the subject at all. (For example, it's 260 pages before the chapter in which he introduces Feynman diagrams starts; in the same number of pages, Peskin and Schroeder have covered all manner of radiative corrections in quantum electrodynamics.)

I'm sure there's a great many discussions of QFT books on here- because it's a hard subject, everybody ends up using several texts to try and get their head around it, and apart from Weinberg (which everyone agrees is uniquely insightful, but a hard slog) and Srednicki (which actually most people seem to like) I can't think of a text that hasn't polarised opinions, so you might like to read around to get a variety of opinions.

 

[king vitamin]

I think you have all the prerequisites (maybe make sure you know the unitary evolution operators and other group theoretical stuff since those are skipped in some quantum texts).

I could give varying opinions on texts, since they're all so divisive, but while we're on the subject of QFT learning material that everyone seems to agree is fantastic, check out Sidney Coleman's video lectures!
http://www.physics.harvard.edu/about/Phys253.html
One of his old TAs took notes, Latexed them, and put them on the arxiv so you can follow along (it can be hard to see the chalkboard)
http://arxiv.org/abs/1110.5013

 

[TeacupPig]

I really liked the lecture notes by David Tong:

http://www.damtp.cam.ac.uk/user/tong/qft.html

 

[homeomorphic]

Aitchinson and Hey all the way. At least, that's the best one I've found so far for a beginner, such as myself.