Quantum Field Theory (Mathematical Surveys and Monographs) [Hardcover]

Gerald B. Folland (Author)

Book Description

Publication Date: August 26, 2008 | ISBN-10: 0821847058 | ISBN-13: 978-0821847053

Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam-Weinberg model of electromagnetic and weak interactions.

Editorial Reviews

Review

Folland's book is valuable for the mathematician who wants to understand how quantum field theory describes nature. ... [This book] is a great introduction to these issues. A mathematician who is serious about learning quantum field theory as a physical theory could do no better than to start with it. Physicists could also benefit from his careful and succinct survey. --SIAM Review

Product Details

• Hardcover: 325 pages
• Publisher: American Mathematical Society (August 26, 2008)
• Language: English
• ISBN-10: 0821847058
• ISBN-13: 978-0821847053
• Product Dimensions: 10.2 x 7.2 x 0.9 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #514,539 in Books (See Top 100 in Books)
  • #98 in Books > Professional & Technical > Professional Science > Physics > Waves & Wave Mechanics

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16 of 16 people found the following review helpful:

5.0 out of 5 stars QFT for Mathematicians, May 17, 2010

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This review is from: Quantum Field Theory (Mathematical Surveys and Monographs) (Hardcover)

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.