Geometry, Topology and Physics: 2nd Edition (Paperback) book cover

Geometry, Topology and Physics

2nd Edition

By Mikio Nakahara

CRC Press

596 pages

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Paperback: 9780750306065
pub: 2003-06-04
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pub: 2017-07-27
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Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields.

The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view.

Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.


"…a very impressive book."

-Australian and New Zealand Physicists

"The clarity of the presentation is enhanced by explicit calculations and diagrams; the proof of a theorem is given only when it is instructive and not very technical. There is also a large number of exercises and problems, and last but not least, an index … superb layout…"

- Zentralblatt fur Mathematick un ihre Grenzgebiete

"I believe that the book will not only boost modernization of the traditional courses of theoretical physics but will prompt the specialist in topology and differential geometry to have a closer look at the applications. So I welcome this second edition."

-Christopher Gilmour

Table of Contents

Quantum Physics

Mathematical Preliminaries

Homology Groups

Homotopy Groups


DeRham Cohomology Groups

Riemannian Geometry

Complex Manifolds

Fibre Bundles

Connections on Fibre Bundles

Characteristic Classes

Index Theorems

Anomalies in Gauge Field Theories

Bosonic String Theory



Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Geometry / General
SCIENCE / Mathematical Physics
SCIENCE / Physics