Differential Geometry for Physicists

Bo-Yu Hou, Bo-Yuan Hou;;;

• Publisher: WSPC
• Year: 1997
• eBook ISBN: 9789813105096
• Topic: Physical Sciences
• Subtopic: Geometry

This book is divided into fourteen chapters, with 18 appendices as introduction to prerequisite topological and algebraic knowledge, etc. The first seven chapters focus on local analysis. This part can be used as a fundamental textbook for graduate students of theoretical physics. Chapters 8–10 discuss geometry on fibre bundles, which facilitates further reference for researchers. The last four chapters deal with the Atiyah-Singer index theorem, its generalization and its application, quantum anomaly, cohomology field theory and noncommutative geometry, giving the reader a glimpse of the frontier of current research in theoretical physics.

Table of contents

• Contents
• Preface
• Chapter 1 Differentiable Manifolds and Differential Forms
• Chapter 2 Transformation of Manifold, Manifolds with Given Vector Fields and Lie Group Manifold
• Chapter 3 Affine Connection and Covariant Differentiation
• Chapter 4 Riemannian Manifold
• Chapter 5 Symplectic Manifold and Contact Manifold
• Chapter 6 Complex Manifolds
• Chapter 7 Homology of Manifolds
• Chapter 8 Homotopy of Manifold,Fibre Bundle, Classification of Fibre Bundles
• Chapter 9 Differential Geometry of Fibre Bundle, Yang-Mills Gauge Theory
• Chapter 10 Characteristic Classes
• Chapter 11 The Atiyah-Singer Index Theorem
• Chapter 12 Index Theorem on Manifold with Boundary and on Open Infinite Manifold
• Chapter 13 Family Index Theorem, Topological properties of Quantum Gauge Theory
• Chapter 14 Noncommutative Geometry, Quantum Group, and q-deformation of Chern-Characters
• Appendix A Simple Introduction to Set Theory
• Appendix B Preliminary Topology
• Appendix C Some Basic Algebraic Structures
• Appendix D Homomorphism of Algebraic Structure and Tensor Algebra
• Appendix E Exact Sequence of Homomorphism
• Appendix F Abelian Group
• Appendix G Stokes' Theorem
• Appendix HQuarternion and Milnor Exotic Spheres
• Appendix IGeneralized Kronecker δ notation
• Appendix J n-dimensional Sphere Sn
• Appendix SU(2) Group Manifold
• Appendix L S2 Manifold and Hopf Maps
• Appendix M Clifford Algebra, Spin Group and its Representations
• Appendix N Good Cover and the Nerve of a Cover. Čech Cohomology
• Appendix O Symmetric Trace
• Appendix P Cohomology with Compact Support and Cohomology on Fibre Bundle, Thorn Class
• Appendix Q K-theory, Topological Invariance of Elliptic Operator
• Appendix R Cohomology of Lie group and Lie algebra
• Appendix some Recursion Relation of Q-BRST Algebra
• References
• Index