Hello, I'm thinking of starting to study some QFT. I know EM and QM on the level of the first part of Griffiths' books on the subject, and I know (classical) mechanics on the level of Marion & Thornton/Taylor, and I know GR on the level of Schutz/Hartle. Are there a few topics in these areas that I should study? (Heisenberg's matrix formulation of QM, Poisson brackets and the Hamilton-Jacobi formulation of classical mechanics, relativistic EM/field tensor/solutions of Maxwell's equations in potential formulation, classical field theory expressed in terms of Lagrangians/Hamiltonians.) What are some good books/online notes to study these? I assume Goldstein for the classical mechanics stuff, and Griffiths for the EM topics? I also remember reading that you need group theory and complex analysis. What topics do you need to study, exactly, and what are some good books/online notes for theses? Are there any other prerequisites? What are some good books for QFT? I heard great things on Amazon for A. Zee's book, and Princeton University Press had posted the first chapter on their website (!), but their explanation of the path integral formulation of QM was confusing... (Is this just me being an idiot, or have others noticed this as well?) (Also, sorry about this being a long-ish post!)
This book that came out recently looks relevant: http://www.amazon.com/Special-Relativity-Feynman-Diagrams-Theoretical/dp/8847015030 For a gentle intro to QFT, I'd recommend the books by Aitchison and Hey. http://www.amazon.com/Gauge-Theories-Particle-Physics-Third/dp/0750308648 Also David Tong's lecture notes http://www.damtp.cam.ac.uk/user/tong/qft.html For mechanics, I like Landau & Lifschitz (watch out for bad printings, though). The complex analysis in Boas should be enough.
I passionately hate that book (2nd edition). I think any other choice would be better. QFT doesn't really have prerequisites, other than knowledge of basic QM of course. There's very little you can do to prepare for it actually. The best way to prepare for it to try to study the first two chapters or so of several QFT books on your own. Regarding group theory and complex analysis, I think you should just make sure that you understand what a group is, and what a representation of a group is. You won't really need complex analysis, but if you're curious about the subject, I think Saff & Snider is very nice for physics students. Regarding electrodynamics, you need to know what Maxwell's equations say, but don't worry about solving them. I don't think anyone explains it well. You will find it confusing no matter what book you read. I don't know if Zee is less or more confusing than others. There are lots of threads where people ask similar questions. You should search for them.
You do need to be able to compute contour integrals, which is why I recommended Boas. She has a pretty good chapter on the subject.
Do you? I can't even remember. It's been a long time since I studied QFT. Anyway, Saff & Snider cover that pretty well too.
Zee's book is probably the most physically motivated description of quantum field theory that is out there. Most textbooks get bogged down on computational techniques (which are quite heavy), and its easy to lose track of whats going on physically. Unfortunately, that is a double-edged-sword. You could work through nearly all of Zee and not be able to calculate much of anything. Zee supplemented by Peskin (which is the current standard use text, as far as I can tell) might be the way to go. I disagree. I began my study of QFT with a very good understanding of Lie groups, which I found to be tremendously useful. Also, you really need to know complex analysis at some level to understand different types of Green's functions (forward, retarded, Feynman), and the pole/branch cut structure is where most of the physics lives.
I'm currently in the process of using my insufficient free time to try to learn QFT. Because I'm a mathematician, and not just any mathematician, but a certain sort of mathematician, the most pleasant way for me to get started seems to be to work through Baez's seminar notes on categorification and quantization (starting in Fall 2003). I have made it through all of it, except for the last couple of lectures in part 3 of the course, in which he actually gets to QFT. It's quite a detour for what seems like such a small pay-off, but it's a very entertaining detour, and if you're like me, the pay-off from those last couple of lectures seems quite significant. http://math.ucr.edu/home/baez/QG.html It takes you fairly far afield, but a spoonful of sugar makes the medicine go down for me (some fantastic math is covered along the way). Also, the Fall 2002 and Spring 2003 notes are very helpful. And maybe the course on gauge theory and topology. Also, there are notes from his classical mechanics and quantum mechanics courses there, too. A less idiosyncratic way to get some intuition is to start with Feynman's QED. Penrose's Road to Reality has some good chapters on the Clifford algebras, the Dirac equation, and QFT that are a good supplement to other sources (but really should be just a supplement). I also tried Zee and I kind of like it and kind of hate it at the same time. I actually thought the explanation of the path-integral formulation was great, but I found the subsequent chapters much less intuitive, unfortunately. So, I've put Zee aside to read Baez's notes (taking the long and indirect, but scenic route) and started reading Aichison and Hey. My favorite book on classical mechanics is V. I. Arnold's.
I would not recommend Zee's book as a first book, because it may be the most intuitive book, pleasant to read, physicaly motivated book on the subject, if you want to learn the methods by calculating (which I think is the best way in physics) you should prefer Peskin & Shcroeder's book, or even more Srednicki's, (you can take a look at a draft of the book on this page: http://web.physics.ucsb.edu/~mark/qft.html ). Zee's nutshell is a really charming book but it can be misleading in the sense that you can easily read and follow the calculus, but when you try to redo them on your own, you realize that you didn't assimilate so well the knowledge. Plus, in my opinion it lacks of central points of QFT: LSZ formula, doesn't emphasize enough on Ward identities, unitarity of non Abelian gauge theories, the Standard Model, renormalization, opens too quickly some really advanced topics (GUT, 4pages on string theory). But it is still a really good book, that you should learn one you'll be more familiar with the methods/mechanics of QFT ;) There still is Weinberg's book if you want to understand why mixing up QM, SR and locality can only lead you to QFT, but you may need more background on group theory for the first chapters.
Stone has a nice set of notes on maths for physics. Chapters 8 & 9 of part II cover complex analysis, with chapter 9 containing lots of common tricks used in physics. http://webusers.physics.illinois.edu/~m-stone5/mma/mma.html http://webusers.physics.illinois.edu/~m-stone5/mmb/mmb.html I'm a biologist, so I don't know QFT to the standard you are probably needing to, but to get the main ideas I did find QFT from a condensed matter viewpoint more intuitive (it's just another way to write Schroedinger's equation in solids). Coleman, http://www.physics.rutgers.edu/~coleman/620/mbody/pdf/bkx.pdf Nayak, http://stationq.cnsi.ucsb.edu/~nayak/courses.html I also found it helpful to read about statistical field theory (SFT), which has a similar formalism to QFT, but where the treatment of renormalization is common sensical. I don't know why QFT books present renormalization in such a mystical way compared to SFT, but Weinberg's, Polchinski's and Hollowood's notes show that renormalization in QFT can also be understood with the same common sense. Kardar, http://ocw.mit.edu/courses/physics/...-physics-of-fields-spring-2008/lecture-notes/ Weinberg, http://ccdb4fs.kek.jp/cgi-bin/img_index?197610218 Polchinski, http://arxiv.org/abs/hep-th/9210046v2 Hollowood, http://arxiv.org/abs/0909.0859
It's a homomorphism from the group into the group of automorphisms of a vector space. So, the group is acting as symmetries of that vector space. For example, the special orthogonal group in its usual representation acts by rotations of Euclidean space, holding the origin fixed.