Amazon.com: Customer Reviews: Quantum Field Theory (Mathematical Surveys and Monographs)
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on May 17, 2010
It is well known that mathematicians and physicists approach advanced mathematics from entirely different quadrants of the universe. This communication gap explains in part why physicists often find it so challenging to learn their requisite mathematics from "pure" mathematicians, and why mathematicians can find it so unbelievably difficult to teach themselves some current theoretical physics by reading books written by physicists, even when they already understand the underlying mathematics quite well.

Among the short list of books which help bridge this chasm (books by authors such as O'Neill, Frankel, Arnol'd, Marsden, Sachs and Wu, etc.), I would now include Gerald Folland's lucid introduction to quantum field theory. The opening sentence in the Preface summarizes Folland's intent perfectly:

"This book is an attempt to present the rudiments of quantum field theory in general and quantum electrodynamics in particular, as actually practiced by physicists for the purpose of understanding the behavior of subatomic particles, in a way that will be comprehensible to mathematicians."

Prospective buyer beware: this book is NOT an elementary introduction for beginners or a self-contained reference that will introduce the mountain of prerequisite mathematics. To read this book, the prospective reader must already be familiar with Fourier analysis, basic functional analysis (esp. Hilbert space theory), distributions, a little Lie theory, the use of manifold theory through the Hamiltonian/Lagrangian approach to classical mechanics, special relativity, and basic quantum mechanics.

Folland's book is especially well-suited to the professional mathematician who is trying to educate himself or herself in the basics of quantum field theory, although it would also be an excellent reference for the physicist who wants to see the mathematics "done right." Mathematicians doing independent study who have already grown frustrated trying to read QFT books by physicists (Weinberg, Zee, Srednicki, Peskin and Schroeder, Kaku, Bjorken and Drell, etc.) will find Folland's book written in a style that is much more familiar and accessible to them.

Professor Folland is to be commended for taking the time and effort to write this unique book. The potential audience for any book on quantum field theory is already quite small, and this book addresses a subset of that already limited group. For those to whom the book is directed, however, it will serve as a truly unique and invaluable reference.
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on June 20, 2015
Extremely useful book. It takes effort to read, but for me it strikes the right balance between rigour and sloppiness. Enough to push my limits, but not make me feel completely swamped by the analysis flying past.

I've frequently referred back to chapters here for an explanation of just what sane concept other QFT books are trying to pretend is trivial. Both approaches are useful, but this book has been the most essential in my understanding.
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on January 17, 2014
This book provides a unique and wonderful treatment of quantum field theory. It is rigorous where the rigor is possible and it tells you when you have to start working rather sloppy and where the dangers (i.e. hidden assumptions) and advantages of the physicists approach are. It is the first QFT book I read that does not leave dozens of open questions in each chapter and also the first book "for mathematicians" that actually covers and explains the physics rather than just the mathematical structure. As a student of math and physics I am deeply grateful to professor Folland for writing this book!
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