物理學中的拓撲和幾何

內(nèi)容概要

拓撲和幾何的概念與方法在物理學中的應用有助于加深人們對物理學的許多重要領域（如凝聚態(tài)物理、宇宙學、此力和粒子物理）的理解，本書是一本關于幾何和拓撲在這些領域中的應用與發(fā)展的高級教材，書中分章節(jié)相對獨立地介紹了規(guī)范理論、BRST量子化、手性異常、超對稱孤子和非交換幾何中的拓撲概念。本書適用于相關專業(yè)的研究生、對本領域感興趣的讀者以及講授相關課程的教師。

作者簡介

作者：(德國)比爾 (德國)斯特芬

書籍目錄

Introduction and Overview  1 Topology and Geometry in Physics  2 An Otuline of the Book  3 Complementary LiteratureTopological 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 ConclusionsAspects of BRST Quantization  1 Symmetries and Constraints  2 Canonical BRST Construction  3 Action Formalism  4 Applications of BRST Methods  Appendix.ConventionsChiral 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 QMSupersymmetric 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  AppendixIndex

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