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Geometry, topology, and physics / Mikio Nakahara

Author
Nakahara, Mikio
Published
Boca Raton, FL : Taylor & Francis Group, [2003]
Copyright Date
©2003
Edition
2nd ed.
Physical Description
xxii, 573 pages : illustrations ; 24 cm.
Additional Creators
Institute of Physics (Great Britain)

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Contents
Quantum physics. Analytical mechanics ; Canonical quantization ; Path integral quantization of a Bose particle ; Harmonic oscillator ; Path integral quantization of a Fermi particle ; Quantization of a scalar field ; Quantization of a Dirac field ; Gauge theories ; Magnetic monopoles ; Instantons -- Mathematical preliminaries. Maps ; Vector spaces ; Topological spaces ; Homeomorphisms and topological invariants -- Homology groups. Abelian groups ; Simplexes and simplicial complexes ; Homology groups of simplicial complexes ; General properties of homology groups -- Homotopy groups. Fundamental groups ; General properties of fundamental groups ; Examples of fundamental groups ; Fundamental groups of polyhedra ; Higher homotopy groups ; General properties of higher homotopy groups ; Examples of higher homotopy groups ; Orders in condensed matter systems ; Defects in nematic liquid crystals ; Textures in superfluid ³He-A -- Manifolds. Manifolds ; The calculus of manifolds ; Flows and lie derivatives ; Differential forms ; Integration of differential forms ; Lie groups and Lie algebras : The action of Lie groups on manifolds ; de Rham cohomology groups. Stokes' theorem ; de Rham cohomology ; Poincaré's lemma ; Structure of de Rham cohomology groups -- Riemannian geometry. Riemannian manifolds and pseudo-Riemannian manifolds ; Parallel transport, connection and covariant derivative ; Curvature and torsion ; Levi-Civita connections ; Holonomy ; Isometries and conformal transformations ; Killing vector fields and conformal Killing vector fields ; Non-coordinate bases ; Differential forms and Hodge theory ; Aspects of general relativity ; Bosonic string theory -- Complex manifolds. Complex manifolds ; Calculus on complex manifolds ; Complex differential forms ; Hermitian manifolds and Hermitian differential geometry ; Kähler manifolds and Kähler differential geometry ; Harmonic forms and [partial]-cohomology groups ; Almost complex manifolds ; Orbifolds -- Fibre bundles. Tangent bundles ; Fibre bundles ; Vector bundles ; Principal bundles -- Connections on fibre bundles. Connections on principal bundles ; Holonomy ; Curvature ; The covariant derivative on associated vector bundles ; Gauge theories ; Berry's phase -- Characteristic Classes. Invariant polynomials and the Chern-Weil homomorphism ; Chern classes ; Chern characters ; Pontrjagin and Euler classes ; Chern-Simmons forms ; Stiefel-Whitney classes -- Index theorems. Elliptic operators and Fredholm operators ; The Atiyah-Singer index theorem ; The de Rham complex ; The Dolbeault complex ; The signature complex ; Spin complexes ; The heat kernel and generalized [zeta]-functions ; The Atiyah-Patodi-Singer index theorem ; Supersymmetric quantum mechanics ; Supersymmetric proof of index theorem -- Anomalies in gauge field theories. Introduction ; Abelian anomalies ; Non-Abelian anomalies ; The Wes-Zumino consistency conditions ; Abelian anomalies versus non-Abelian anomalies ; The parity anomaly in odd-dimensional spaces -- Bosonic string theory. Differential geometry on Riemann surfaces ; Quantum theory of bosonic strings ; One-loop amplitudes.
Summary
"Geometry, Topology and Physics is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics."--BOOK JACKET.
Subject(s)
ISBN
0750306068 (Softcover)
9780750306065 (Softcover)
Bibliography Note
Includes bibliographical references (pages 560-564) and index.
View MARC record | catkey: 2606005