Geometry, topology and physics

M. Nakahara

594 pages, parution le 25/06/2003 (2^eme édition)

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Résumé

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 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 with which the reader is assumed to be familiar. Chapter 2 introduces the mathematical concepts to be used throughout, namely maps, vector spaces and topology.

Chapters 3-8 introduce the more elaborate concepts in geometry and topology - Homology and Homotopy groups, Manifolds, De Rham Cohomology groups, Riemannian Geometry and Complex Manifolds - discussing in the appropriate context the application of these concepts to liquid crystals, superfluid Helium, General Relativity and Bosonic String Theory.

Chapters 9-12 unify geometry and topology, with the introduction of fibre 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 of the book 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 is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

Quantum physics
Mathematical preliminaries
Homology groups
Homotopy groups
Manifolds
De Rham cohomology groups
Riemannian geometry
Complex manifolds
Fibre bundles
Connections on fibre bundles
Characteristic classes
Index theorems
Anomalies in gauge field theories
Bosonic string theory

References
Index

L'auteur - M. Nakahara

Department of Mathematics and Physics, Kinki University, Japan

Caractéristiques techniques

	PAPIER
Éditeur(s)	Institute of Physics (IOP)
Auteur(s)	M. Nakahara
Parution	25/06/2003
Édition	2^eme édition
Nb. de pages	594
Format	15,5 x 23,5
Couverture	Broché
Poids	1025g
Intérieur	Noir et Blanc
EAN13	9780750306065
ISBN13	978-0-7503-0606-5