**Mathematical Surveys and Monographs**

Volume: 149;
2008;
325 pp;
Hardcover

MSC: Primary 81;

Print ISBN: 978-0-8218-4705-3

Product Code: SURV/149

List Price: $97.00

AMS Member Price: $77.60

MAA Member Price: $87.30

**Electronic ISBN: 978-1-4704-1376-7
Product Code: SURV/149.E**

List Price: $97.00

AMS Member Price: $77.60

MAA Member Price: $87.30

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#### Supplemental Materials

# Quantum Field Theory: A Tourist Guide for Mathematicians

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*Gerald B. Folland*

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.

#### Readership

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

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Quantum Field Theory: A Tourist Guide for Mathematicians

- Contents iii4 free
- Preface v6 free
- Chapter 1. Prologue 112 free
- Chapter 2. Review of Pre-quantum Physics 1324
- Chapter 3. Basic Quantum Mechanics 3344
- Chapter 4. Relativistic Quantum Mechanics 6576
- Chapter 5. Free Quantum Fields 97108
- Chapter 6. Quantum Fields with Interactions 123134
- Chapter 7. Renormalization 191202
- Chapter 8. Functional Integrals 257268
- Chapter 9. Gauge Field Theories 291302
- Bibliography 317328
- Index 323334 free