Research Catalog

Topology, geometry, and gauge fields : interactions

Title
Topology, geometry, and gauge fields : interactions / Gregory L. Naber.
Author
Naber, Gregory L., 1948-
Publication
New York : Springer, ©2000.

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Details

Description
xiii, 443 pages; 25 cm.
Series Statement
Applied mathematical sciences ; v. 141
Uniform Title
Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 141.
Subject
  • Topology
  • Geometry
  • Gauge fields (Physics)
  • Mathematical physics
  • geometry
  • Geometry
  • Mathematical physics
  • Topology
  • Topologie
  • Geometrie
  • Eichfeld
  • Algebraïsche topologie
  • Veldentheorie
  • Mathematische fysica
  • Topologie
  • Géométrie
  • Champs de jauge (physique)
  • Physique mathématique
Bibliography (note)
  • Includes bibliographical references and index.
Contents
Ch. 1. Geometrical Background -- 1.1. Smooth Manifolds and Maps -- 1.2. Matrix Lie Groups -- 1.3. Principal Bundles -- 1.4. Connections and Curvature -- 1.5. Associated Bundles and Matter Fields -- Ch. 2. Physical Motivation -- 2.1. General Framework For Classical Gauge Theories -- 2.2. Electromagnetic Fields -- 2.3. Spin Zero Electrodynamics -- 2.4. Spin One-Half Electrodynamics -- 2.5. SU (2)-Yang-Mills-Higgs Theory on R[Superscript n] -- Ch. 3. Frame Bundles and Spacetimes -- 3.1. Partitions of Unity, Riemannian Metrics and Connections -- 3.2. Continuous Versus Smooth -- 3.3. Frame Bundles -- 3.4. Minkowski Spacetime -- 3.5. Spacetime Manifolds and Spinor Structures -- Ch. 4. Differential Forms and Integration -- 4.1. Multilinear Alegbra -- 4.2. Vector-Valued Forms -- 4.3. Differential Forms -- 4.4. The de Rham Complex -- 4.5. Tensorial Forms -- 4.6. Integration on Manifolds -- 4.7. Stokes' Theorem -- Ch. 5. de Rham Cohomology -- 5.1. The de Rham Cohomology Groups -- 5.2. Induced Homomorphisms -- 5.3. Cochain Complexes and Their Cohomology -- 5.4. The Mayer- Vietoris Sequence -- 5.5. The Cohomology of Compact, Orientable Manifolds -- 5.6. The Brouwer Degree -- 5.7. The Hopf Invariant -- Ch. 6. Characteristic Classes -- 6.1. Motivation -- 6.2. Algebraic Preliminaries -- 6.3. The Chern-Weil Homomorphism -- 6.4. Chern Numbers -- 6.5. Z[Subscript 2]-Cech Cohomology for Smooth Manifolds -- Appendix. Seiberg-Witten Monopoles on R[Superscript 4].
ISBN
  • 0387989471
  • 9780387989471
LCCN
  • 99052753
  • 9780387989471
OCLC
  • ocm42649825
  • 42649825
  • SCSB-1237232
Owning Institutions
Princeton University Library