Topology and Geometry for Physicists

by Charles Nash, Siddhartha Sen

Overview

Differential geometry and topology are essential tools for many theoretical physicists, particularly in the study of condensed matter physics, gravity, and particle physics. Written by physicists for physics students, this text introduces geometrical and topological methods in theoretical physics and applied mathematics. It assumes no detailed background in topology or geometry, and it emphasizes physical motivations, enabling students to apply the techniques to their physics formulas and research.
"Thoroughly recommended" by The Physics Bulletin, this volume's physics applications range from condensed matter physics and statistical mechanics to elementary particle theory. Its main mathematical topics include differential forms, homotopy, homology, cohomology, fiber bundles, connection and covariant derivatives, and Morse theory.

Product Details

ISBN-13:	9780486478524
Publisher:	Dover Publications
Publication date:	02/17/2011
Series:	Dover Books on Mathematics
Edition description:	Reprint
Pages:	320
Sales rank:	788,609
Product dimensions:	5.30(w) x 8.40(h) x 1.00(d)

About the Author

Charles Nash is a Professor of Mathematics at the National University of Ireland. His main research interests are quantum field theory and differential topology.
Siddhartha Sen is Professor Emeritus in Applied Mathematics at the University College of Dublin.

Table of Contents

Preface
1. Basic Notions of Topology and the Value of Topological Reasoning
2. Differential Geometry: Manifolds and Differential Forms
3. The Fundamental Group
4. The Homology Groups
5. The Higher Homotopy Groups
6. Cohomology and De Rhan Cohomology
7. Fibre Bundles and Further Differential Geometry
8. Morse Theory
9. Defects, Textures, and NHomotopy Theory
10. Yang-Mills Theories: Instantons and Monopoles
Further Reading
Subject Index