Overview

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.

Full Product Details

Author:   Albert S. Schwarz ,  E. Yankowsky ,  S. Levy
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 1993
Volume:   307
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783642081309

ISBN 10:   3642081304
Pages:   276
Publication Date:   09 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Definitions and Notations.- 1 The Simplest Lagrangians.- 2 Quadratic Lagrangians.- 3 Internal Symmetries.- 4 Gauge Fields.- 5 Particles Corresponding to Nonquadratic Lagrangians.- 6 Lagrangians of Strong, Weak and Electromagnetic Interactions.- 7 Grand Unifications.- 8 Topologically Stable Defects.- 9 Topological Integrals of Motion.- 10 A Two-Dimensional Model. Abrikosov Vortices.- 11 ’t Hooft—Polyakov Monopoles.- 12 Topological Integrals of Motion in Gauge Theory.- 13 Particles in Gauge Theories.- 14 The Magnetic Charge.- 15 Electromagnetic Field Strength and Magnetic Charge in Gauge Theories.- 16 Extrema of Symmetric Functionals.- 17 Symmetric Gauge Fields.- 18 Estimates of the Energy of a Magnetic Monopole.- 19 Topologically Non-Trivial Strings.- 20 Particles in the Presence of Strings.- 21 Nonlinear Fields.- 22 Multivalued Action Integrals.- 23 Functional Integrals.- 24 Applications of Functional Integrals to Quantum Theory.- 25 Quantization of Gauge Theories.- 26 Elliptic Operators.- 27 The Index and Other Properties of Elliptic Operators.- 28 Determinants of Elliptic Operators.- 29 Quantum Anomalies.- 30 Instantons.- 31 The Number of Instanton Parameters.- 32 Computation of the Instanton Contribution.- 33 Functional Integrals for a Theory Containing Fermion Fields.- 34 Instantons in Quantum Chromodynamics.- 35 Topological Spaces.- 36 Groups.- 37 Gluings.- 38 Equivalence Relations and Quotient Spaces.- 39 Group Representations.- 40 Group Actions.- 41 The Adjoint Representation of a Lie Group.- 42 Elements of Homotopy Theory.- 43 Applications of Topology to Physics.- Bibliographical Remarks.- References.

Reviews

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

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

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions