Which QFT Book Should I Choose for a Deep Theoretical Understanding?

[Kontilera]

Hello! I´m currenly considering buying a complete QFT book, I have done some classical field theory and glossed around in Zee's nutshell book. I also have knowledge from advanced QM up to Klein Gordon eqn and 2nd quantization. My question is now which one you think will fit me the best, my economy allows Peskin and Schröder or the first two books of Weinberg trilogogy.

My situation is the following:
I have a big interest for mathematical physics - I am now reading MTW - 'Gravitation' and likes the chapters about differential forms and the boundary of a boundary. The computational parts and not so important techniques for calculating cross sections is however not so funny to read. I want a deep understanding for the basic assumptions and methods of QFT. (I´m not a purist, verifying every derivation but I like to se how the words of physics can be put in very elegant equations.)

I will take a QFT course later on in my "career" so I think I can allow myself to prioritate the interesing parts of the theory now and focus on more calculational parts in the future, with my teacher.

Is my descprition most accurate for Weinbergs book or Peskin and Schröders book?If you want to recommend any other book feel free to do it! :)

 

[Bill_K]

Zee takes difficult topics and makes them look easy. Weinberg takes easy topics and makes them look difficult. Go for Peskin and Schroder!

 

[kloptok]

Or Srednickis book, which I prefer over Peskin & Schroeder. My ideal combo would be Zee and Srednicki! Srednicki for calculations and Zee for concepts.

 

[vanhees71]

This question is less easy to answer than one might think. There are a lot of textbooks on qft out there.

Zee is out of the question. It's nice to read if you know already the subject, but it's pretty superficial in many things, and I don't think that one can comprehend what is qft about as a beginner from this book, let alone how to do calculations. The latter point is very important since QFT starts to become familiar only if one can do real calculations.

Peskin, Schroeder is good to start with. You learn the basics and, most important for the beginning, how to do calculations, i.e., how to evaluate Feynman diagrams. It's less good for a deeper understanding, and there are many sloppy things like logarithms with a dimensionful argument (and that in the chapter about renormalization!).

My clear favorite are Weinberg's marvelous books (on any topic, including the three volumes on qft, gravity (GRT), and cosmology). It might be true that it looks not as the easiest way to start learning qft, but many things just look different, because Weinberg carefully explains why qft is the way it is, starting from the Poincare group (here giving a complete treatment for fields with arbitrary spin, including a complete proof of fundamental things like PCT theorem and spin-statistics connection). Other highlights are the treatment of IR issues in Vol. I and non-abelian gauge theories (including background field gauge) in Vol. II. Anyway, it's a must-read for the advanced student and scholar.

Another book I like very much is Ryder, Quantum Field Theory. I think that's the right thing to start with. Particularly nice is the treatment of the Dirac Equation in the beginning, Ward-Takahashi identities in gauge theories. Also one can learn how to calculate Feynman diagrams, including loop diagrams and renormalization.

The path-integral approach is very nicely treated in Bailin and Love, Gauge Theories.

Srednicky is also a very good book. I'd prefer it compared to Peskin/Schroeder. I only don't understand, why it treats $\phi^3$ theory at length also this is for sure an ill-defined model to begin with. However, one learns how to calculate Feynman diagrams pretty well with this approach without being disturbed by a lot of formal complications like gauge invariance in the beginning. However, since one has to learn these subjects anyway and since it's real physics (which is more fun than to just calculate physically irrelevant loop diagrams) why doesn't he use spinor QED which is not much more complicated from the topological structure of the Feynman diagrams, because also there is only a three-particle vertex.

 

[Kontilera]

Thanks for your responses! What do you think about the two volume set of 'Gauge theories in particle physics' by Aitchison and Hey? Any pro's or cons?

 

[yenchin]

You might want to start with David Tong's QFT notes: http://www.damtp.cam.ac.uk/user/tong/qft.html.

 

[A. Neumaier]

Hello! I´m currenly considering buying a complete QFT book, I have done some classical field theory and glossed around in Zee's nutshell book. I also have knowledge from advanced QM up to Klein Gordon eqn and 2nd quantization. My question is now which one you think will fit me the best, my economy allows Peskin and Schröder or the first two books of Weinberg trilogy.

I have a big interest for mathematical physics

Given your interest in mathematical physics, Weinberg is far superior to any of the other QFT books, as it is closest to being mathematically precise and elegant.

You might also want to look into Zeidler's QFT books, as they try to bridge the gulf between mathematicians and physicists in a way no one else does.

 

[omephy]

Just stay away from Srednicki's book.

 

[Daverz]

Thanks for your responses! What do you think about the two volume set of 'Gauge theories in particle physics' by Aitchison and Hey? Any pro's or cons?

I only have the first volume, but it's excellent.

I'd start there and with Tong's online notes.

Another good book that's not often mentioned is Nair, Quantum Field Theory: A Modern Perspective

Srednicki reads more like a workbook than a text. That's a useful approach when you're getting the necessary background in class and don't need a lot of verbiage.