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Quantum Field Theory and Topology

  • Book
  • © 1993

Overview

Authors:
  1. Albert S. Schwarz

    1. Department of Mathematics, 565 Kerr Hall, University of California, Davis, USA

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Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 307)

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Table of contents (45 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    1. Introduction

      • Albert S. Schwarz
      Pages 1-5

  3. Definitions and Notations

    1. Definitions and Notations

      • Albert S. Schwarz
      Pages 6-9

  4. The Basic Lagrangians of Quantum Field Theory

    1. Front Matter

      Pages 11-11
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    2. The Simplest Lagrangians

      • Albert S. Schwarz
      Pages 13-16

    3. Quadratic Lagrangians

      • Albert S. Schwarz
      Pages 17-18

    4. Internal Symmetries

      • Albert S. Schwarz
      Pages 19-23

    5. Gauge Fields

      • Albert S. Schwarz
      Pages 24-27

    6. Particles Corresponding to Nonquadratic Lagrangians

      • Albert S. Schwarz
      Pages 28-29

    7. Lagrangians of Strong, Weak and Electromagnetic Interactions

      • Albert S. Schwarz
      Pages 30-36

    8. Grand Unifications

      • Albert S. Schwarz
      Pages 37-39

  5. Topological Methods in Quantum Field Theory

    1. Front Matter

      Pages 41-41
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    2. Topologically Stable Defects

      • Albert S. Schwarz
      Pages 43-55

    3. Topological Integrals of Motion

      • Albert S. Schwarz
      Pages 56-61

    4. A Two-Dimensional Model. Abrikosov Vortices

      • Albert S. Schwarz
      Pages 62-67

    5. ’t Hooft—Polyakov Monopoles

      • Albert S. Schwarz
      Pages 68-73

    6. Topological Integrals of Motion in Gauge Theory

      • Albert S. Schwarz
      Pages 74-79

    7. Particles in Gauge Theories

      • Albert S. Schwarz
      Pages 80-82

    8. The Magnetic Charge

      • Albert S. Schwarz
      Pages 83-88

    9. Electromagnetic Field Strength and Magnetic Charge in Gauge Theories

      • Albert S. Schwarz
      Pages 89-93
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Keywords

About this book

In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.

Reviews

"This is a very interesting book on an important topic both for physics and for mathematics." - Bulletin of the London Mathematic Society

Authors and Affiliations

  • Department of Mathematics, 565 Kerr Hall, University of California, Davis, USA

    Albert S. Schwarz

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