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Quantum Field Theory: A Tourist Guide for Mathematicians
Gerald B. Folland, University of Washington, Seattle, WA
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Mathematical Surveys and Monographs
2008; 325 pp; hardcover
Volume: 149
ISBN-10: 0-8218-4705-8
ISBN-13: 978-0-8218-4705-3
List Price: US$97 Member Price: US$77.60
Order Code: SURV/149

Quantum Fields and Strings: A Course for Mathematicians - Pierre Deligne, Pavel Etingof, Daniel S Freed, Lisa C Jeffrey, David Kazhdan, John W Morgan, David R Morrison and Edward Witten

Quantum Mechanics for Mathematicians - Leon A Takhtajan

Topological Quantum Computation - Zhenghan Wang

Renormalization and Effective Field Theory - Kevin Costello

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.

Graduate students and research mathematicans interested in mathematical physics, specifically, quantum field theory.

Reviews

"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

"The style of the present monograph is clear and the author is honest about possible mathematical shortcomings of quantum field theory."

-- Mathematical Reviews