物理学中的拓扑和几何

出版社:科学
出版日期:2007-4
ISBN:9787030187864
作者:E.Bick,F.D.Stef
页数:358页

内容概要

作者:(德国)比尔 (德国)斯特芬

书籍目录

Introduction and OverviewE.Bick, F.D.Steffen1、Topology and Geometry in Physics2、An Outline of the Book3、Complementary LiteratureTopological Concepts in Gauge TheoriesF.Lenz1、Introduction2、Nielsen-Olesen Vortex  2.1  Abelian Higgs Model  2.2  Topological Excitations3、Homotopy  3.1  The Fundamental Group  3.2  Higher Homotopy Groups  3.3  Quotient Spaces  3.4  Degree of Maps  3.5  Topological Groups  3.6  Transformation Groups  3.7  Defects in Ordered Media4、Yang-Mills Theory5、't Hooft-Polyakov Monopole  5.1  Non-Abelian Higgs Model  5.2  The Higgs Phase  5.3  Topological Excitations6、Quantization of Yang-Mills Theory7、Instantons  7.1  Vacuum Degeneracy  7.2  Tunneling  7.3  Fermions in Topologically Non-trivial Gauge Fields  7.4  Instanton Gas  7.5  Topological Charge and Link Invariants8、Center Symmetry and Confinement  8.1  Gauge Fields at Finite Temperature and Finite Extension  8.2  Residual Gauge Symmetries in QED  8.3  Center Symmetry in SU(2) Yang-Mills Theory  8.4  Center Vortices  8.5  The Spectrum of the SU(2) Yang-Mills Theory9、QCD in Axial Gauge  9.1  Gauge Fixing  9.2  Perturbation Theory in the Center-Symmetric Phase  9.3  Polyakov Loops in the Plasma Phase  9.4  Monopoles  9.5  Monopoles and Instantons  9.6  Elements of Monopole Dynamics  9.7  Monopoles in Diagonalization Gauges10、ConclusionsAspects of BRST QuantizationJ.W.van Holten1、Symmetries and Constraints  1.1  Dynamical Systems with Constraints  1.2  Symmetries and Noether's Theorems  1.3  Canonical Formalism  1.4  Quantum Dynamics  1.5  The Relativistic Particle  1.6  The Electro-magnetic Field  1.7  Yang-Mills Theory  1.8  The Relativistic String2、Canonical BRST Construction  2.1  Grassmann Variables  2.2  Classical BRST Transformations  2.3  Examples  2.4  Quantum BRST Cohomology  2.5  BRST-Hodge Decomposition of States  2.6  BRST Operator Cohomology  2.7  Lie-Algebra Cohomology3、Action Formalism  3.1  BRST Invariance from Hamilton's Principle  3.2  Examples  3.3  Lagrangean BRST Formalism  3.4  The Master Equation  3.5  Path-Integral Quantization4、Applications of BRST Methods  4.1  BRST Field Theory  4.2  Anomalies and BRST CohomologyAppendix.ConventionsChiral Anomalies and TopologyJ.Zinn-Justin1、Symmetries, Regularization, Anomalies2、Momentum Cut-Off Regularization  2.1  Matter Fields:Propagator Modification  2.2  Regulator Fields  2.3  Abelian Gauge Theory  2.4  Non-Abelian Gauge Theories3、Other Regularization Schemes  3.1  Dimensional Regularization  3.2  Lattice Regularization  3.3  Boson Field Theories  3.4  Fermions and the Doubling Problem4、The Abelian Anomaly  4.1  Abelian Axial Current and Abelian Vector Gauge Fields  4.2  Explicit Calculation  4.3  Two Dimensions  4.4  Non-Abelian Vector Gauge Fields and Abelian Axial Current  4.5  Anomaly and Eigenvalues of the Dirac Operator5、Instantons, Anomalies, and θ-Vacua  5.1  The Periodic Cosine Potential  5.2  Instantons and Anomaly:CP(N-1) Models  5.3  Instantons and Anomaly:Non-Abelian Gauge Theories  5.4  Fermions in an Instanton Background6、Non-Abelian Anomaly  6.1  General Axial Current  6.2  Obstruction to Gauge Invariance  6.3  Wess-Zumino Consistency Conditions7、Lattice Fermions:Ginsparg-Wilson Relation  7.1  Chiral Symmetry and Index  7.2  Explicit Construction:Overlap Fermions8、Supersymmetric Quantum Mechanics and Domain Wall Fermions  8.1  Supersymmetric Quantum Mechanics  8.2  Field Theory in Two Dimensions  8.3  Domain Wall FermionsAppendix A. Trace Formula for Periodic PotentialsAppendix B. Resolvent of the Hamiltonian in Supersymmetric QMSupersymmetric Solitons and TopologyM.Shifman1、Introduction2、D= 1+1;N=1  2.1  Critical(BPS) Kinks  2.2  The Kink Mass (Classical)  2.3  Interpretation of the BPS Equations.Morse Theory  2.4  Quantization.Zero Modes:Bosonic and Fermionic  2.5  Cancelation of Nonzero Modes  2.6  Anomaly Ⅰ  2.7  Anomaly Ⅱ(Shortening Supermultiplet Down to One State)3、Domain Walls in (3+1)-Dimensional Theories  3.1  Superspace and Superfields  3.2  Wess Zumino Models  3.3  Critical Domain Walls  3.4  Finding the Solution to the BPS Equation  3.5  Does the BPS Equation Follow from the Second Order Equation of Motion?  3.6  Living on a Wall4、Extended Supersymmetry in Two Dimensions:The Supersymmetric CP(1) Model  4.1  Twisted Mass  4.2  BPS Solitons at the Classical Level  4.3  Quantization of the Bosonic Moduli  4.4  The Soliton Mass and Holomorphy  4.5  Switching On Fermions  4.6  Combining Bosonic and Fermionic Moduli5、ConclusionsAppendix A. CP(1) Model=O(3) Model (Af=1 Superfields N)Appendix B. Getting Started (Supersymmetry for Beginners)  B.1  Promises of Supersymmetry  B.2  Cosmological Term  B.3  Hierarchy ProblemForces from Connes' GeometryT.Schiicker1、Introduction2、Gravity from Riemannian Geometry  2.1  First Stroke:Kinematics  2.2  Second Stroke:Dynamics3、Slot Machines and the Standard Model  3.1  Input  3.2  Rules  3.3  The Winner  3.4  Wick Rotation4、Connes' Noncommutative Geometry  4.1  Motivation:Quantum Mechanics  4.2  The Calibrating Example:Riemannian Spin Geometry  4.3  Spin Groups5、The Spectral Action  5.1  Repeating Einstein's Derivation in the Commutative Case  5.2  Almost Commutative Geometry  5.3  The Minimax Example  5.4  A Central Extension6、Connes' Do-It-Yourself Kit  6.1  Input  6.2  Output  6.3  The Standard Model  6.4  Beyond the Standard Model7、Outlook and ConclusionAppendix  A.1 Groups  A.2 Group Representations  A.3 Semi-Direct Product and Poincare Group  A.4 AlgebrasIndex

作者简介

《物理学中的拓扑和几何(影印版)》主要内容包括:拓扑和几何的概念与方法在物理学中的应用有助于加深人们对物理学的许多重要领域(如凝聚态物理、宇宙学、引力和粒子物理)的理解,《物理学中的拓扑和几何(影印版)》是一本关于几何和拓扑在这些领域中的应用与发展的高级教材,书中分章节相对独立地介绍了规范理论、BRST量子化、手性异常、超对称孤子和非交换几何中的拓扑概念。《物理学中的拓扑和几何(影印版)》适用于相关专业的研究生、对本领域感兴趣的读者以及讲授相关课程的教师。

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精彩短评 (总计12条)

  •     这本书质量不错,挺好的
  •     这个系列的书印刷质量很一般,价格很贵
  •     好书,没什么可说的.对于搞物理的来说,看纯数学的书未免有些不适应,这本书更加适合我.
  •     感觉有点难度,没怎么看
  •     这个不是一本教科书,就是一本演讲集。收录了几位专家关于拓扑学和微分几何在物理中【主要是量子场论】的应用的文章。内容比较高端,适合有一定基础的童鞋看。
  •     做理论物理并且对数学感兴趣的人用得上。
  •     很不错的书,为以后的进一步深造有很大帮助
  •     在理解了规范场的基础上阅读,会有不少收获。
  •     几何对于物理是很重要的
  •     很清楚
    应当是本经典教材!
  •     这是科学出版社出版的国外物理名著丛书里的一本,原著是德国斯普林格出版社2005年版.拓扑和几何的概念在物理学中的应用很广,本书介绍了规范场理论,BRST量子化,超对称孤子和非交换几何中的拓扑概念,是经典名著.当当服务很好.科学出版社的国外物理名著丛书是经过精心挑选的经典名著,如:狄拉克的量子力学.而且印刷和装帧都非常精美.相比较,世界图书出版公司引进的国外原著影印本质量很差,印刷和装帧就象盗版书,但定价奇贵.
  •     i love it.
 

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