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.

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Specifications

Country

USA

Author

Gerald B. Folland

Binding

Hardcover

EAN

9780821847053

ISBN

0821847058

IsEligibleForTradeIn

1

Label

American Mathematical Society

Manufacturer

American Mathematical Society

MPN

Illustrations

NumberOfItems

1

NumberOfPages

325

PartNumber

Illustrations

PublicationDate

2008-08-26

Publisher

American Mathematical Society

Studio

American Mathematical Society

Most Helpful Customer Reviews

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...
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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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