Quantum Field Theory for Mathematicians (Encyclopedia of Mathematics and its Applications)

Rating:
Summary: fills a niche
Review: This book is far from perfect, but I think it begins to fill an important niche in the world of QFT books: it presents most aspects of the theory, from basic principles to Feynman rules, gauge fields and renormalization, in a form that is unusually accessible to mathematicians. I'm coming at this from the perspective of a mathematician who has tried and failed to learn QFT from a variety of other books, and I wish I had discovered this one before even opening Weinberg or Peskin & Schroeder. Ticciati doesn't completely avoid the kind logical sleight of hand that is commonplace among physicists, but when doing manipulations whose mathematical basis is questionable, he's usually at least honest enough to point this out to the reader. I especially enjoyed the chapter on Lie algebra representation theory, which is closer to a mathematician's presentation of this subject than a physicist's, yet not without plenty of physical motivation. I'd criticize this book only for two things: (1) it's riddled with misprints (some obvious, some not) and (2) some topics are explained rather more concisely than they deserve, and not always in the most logical order; Ticciati has a tendency to use certain subtle concepts implicitly a few sections before he defines them precisely. One may hope that such errors will be corrected in a future edition.

Rating:
Summary: A Great Field Theory Book
Review: Yes this book isn't perfect, but what book on physics is? That aside, there is no question this is an excellent field theory book with a rigorous approach. Physicists could learn from this style to produce better textbooks rather than following their usual mysterious approach to writing. This book is clearly laid out not only in mathematical style but also with clear and concise explanations of many physical concepts. It is in my opinion far better than Weinberg's book, written in a more readable style. It is also better than books like Peskin and Schroeder and Kaku which seem sloppily put together. Put the book together with Ryder and you will have the tools needed to get a good understanding of field theory. The title might be unfortunate, because it might keep physics professors from considering using it in their classes instead of the usual lousy standby's, which is too bad for the students.