Introduction and Overview 1 Topology and Geometry in Physics 2 An Otuline of the Book 3 Complementary Literature Topological Concepts in Gauge Theories 1 Introduction 2 Nielsen-Olesen Vortex 3 Homotopy 4 Yang-Mills Theory 5 't Hooft-Polyakov Monpoloe 6 Quantization of Yang-Mills Theory 7 Instantons 8 Center Symmetry and Confinement 9 QCD in Axial Gauge 10 Conclusions Aspects of BRST Quantization 1 Symmetries and Constraints 2 Canonical BRST Construction 3 Action Formalism 4 Applications of BRST Methods Appendix.Conventions Chiral Anomalies and Topology 1 Symmetries Regularization Anomalies 2 Momentum Cut-Off Regularization 3 Other Regularization Schemes 4 The Abelian Anomaly 5 Instantons Anomalies and θ-Vacua 6 Non-Abelian Anomaly 7 Lattice Fermions:Ginsparg-Wilson Relation 8 Supersymmetric Quantum Mechanics and Domain Wall Fermions Appendix A.Trace Formula for Periodic Potentials Appendix B.Resolvent of the Hamiltonian in Supersymmetric QM Supersymmetric Solitons and Topology 1 Introduction 2 D=1+1；N=1 3 Domain Walls in(3+1)-Dimensional Theories 4 Extended Supersymmetry in Two Dimensions:The Supersymmetric CP(1)Model 5 Conclusions Appendix A.CP(1)Model+O(3)Model(N=1Superfields N) Appendix B.Getting Started (Supersymmetry for Beginners) Forces from Connes Geometry 1 Introdution 2 Gravity from Riemannian Geometry 3 Slot Machines and the Standard Model 4 Connes Noncommutative Geometry 5 The Spectral Action 6 Connes Do-It-Yourself Kit 7 Outlook and Conclusion Appendix Index
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