Product Description

This book provides an introduction to the ideas and techniques of differential geometry and topology. It starts with a brief survey of quantum field theory, gauge theory, general relativity, vector spaces, and topology. Using many illustrations, exercises, and problems, the author demonstrates more elaborate concepts of topology and geometry, including 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 examine anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view.

Product Details

• Amazon Sales Rank: #310893 in Books
• Published on: 2002-09
• Original language: English
• Number of items: 1
• Binding: Paperback
• 596 pages

Review
"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

From the Back Cover
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.

Customer Reviews

Good graduate intro to Differential Geom
To complete this book, there should be a section on general curvilinear coordinate transformations, the ultimate foundation of tensor calculus.This is a defficiency this book shares with many differential geometry texts.But maybe this can be forgiven at graduate level, for which this book is a decent pedagogical text- if a little terse at times.

The book begins with a survey of those areas of physics to which diff geom are applied , then develops some topology, and goes on to a comprehensive discussion of the theory of finite dimensional manifolds-including a chapter on complex manifolds.You will learn basic exterior calculus, lie derivatives and covariant derivatives , and so on.A first choice for those who have had a little preparation at undergraduate level.

One of the best places to start...
Nakahara's book is one of the best introductions to geometry and topology that I have read. I constantly use the book as the starting place for just about any topic in geometry and topolgy.

After reading the book you will not be able to jump straight into research work, but it does bridge the gap between more advanced texts and papers.

Everybody should have a copy.