Geometry, Topology and Physics, Second EditionCRC Press, 04.06.2003 - 596 Seiten 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. |
Inhalt
Quantum Physics | 1 |
Mathematical Preliminaries | 67 |
Homology Groups | 93 |
Homotopy Groups | 121 |
Manifolds | 169 |
de Rham Cohomology Groups | 226 |
Riemannian Geometry | 244 |
Complex Manifolds | 308 |
Fibre Bundles | 348 |
Connections on Fibre Bundles | 374 |
Characteristic Classes | 419 |
Index Theorems | 453 |
Anomalies in Gauge Field Theories | 501 |
528 | |
560 | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
action algebra basis boundary called chart Chern cohomology complex manifold components compute covariant derivative curvature curve defined definition denoted differential dim ker Dirac eigenvalue element equation equivalence class Euler characteristic example Exercise fibre bundle figure follows fundamental group gauge potential given GL(n Grassmann Hamiltonian hence Hermitian holomorphic homeomorphic homology groups horizontal lift index theorem inner product invariant isomorphic Kähler Kähler manifold Lagrangian Let us consider Levi-Civita connection Lie group linear loop map f map ƒ matrix metric Note obtain one-form operator parallel transport parameter path integral PoP1 principal bundle Proof r-form Riemannian satisfies Show structure subgroup symmetry tangent tensor topological space transformation transition function trivial vanishes vector bundle vector field vector space verify μν
Beliebte Passagen
Seite iii - Supersymmetric Gauge Field Theory and String Theory D BAILIN and A LOVE Mechanics of Deformable Media AB BHATIA and RN SINGH...
Verweise auf dieses Buch
A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics Eric Poisson Eingeschränkte Leseprobe - 2004 |
The N: From Calabi-Yau Manifolds to Topological Field-theories P. Fr ,Paolo Soriani Eingeschränkte Leseprobe - 1995 |