物理学中的拓扑和几何 影印版 英文【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

物理学中的拓扑和几何 影印版 英文PDF格式电子书版下载

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Introduction and Overview&E.Bick,F.D.Steffen1

1 Topology and Geometry in Physics1

2 An Outline of the Book2

3 Complementary Literature4

Topological Concepts in Gauge Theories&F.Lenz7

1 Introduction7

2 Nielsen-Olesen Vortex9

2.1 Abelian Higgs Model9

2.2 Topological Excitations14

3 Homotopy19

3.1 The Fundamental Group19

3.2 Higher Homotopy Groups24

3.3 Quotient Spaces26

3.4 Degree of Maps27

3.5 Topological Groups29

3.6 Transformation Groups32

3.7 Defects in Ordered Media34

4 Yang-Mills Theory38

5 't Hooft-Polyakov Monopole43

5.1 Non-Abelian Higgs Model43

5.2 The Higgs Phase45

5.3 Topological Excitations47

6 Quantization of Yang-Mills Theory51

7 Instantons55

7.1 Vacuum Degeneracy55

7.2 Tunneling56

7.3 Fermions in Topologically Non-trivial Gauge Fields58

7.4 Instanton Gas60

7.5 Topological Charge and Link Invariants62

8 Center Symmetry and Confinement64

8.1 Gauge Fields at Finite Temperature and Finite Extension65

8.2 Residual Gauge Symmetries in QED66

8.3 Center Symmetry in SU(2)Yang-Mills Theory69

8.4 Center Vortices71

8.5 The Spectrum of the SU(2) Yang-Mills Theory74

9 QCD in Axial Gauge76

9.1 Gauge Fixing76

9.2 Perturbation Theory in the Center-Symmetric Phase79

9.3 Polyakov Loops in the Plasma Phase83

9.4 Monopoles86

9.5 Monopoles and Instantons89

9.6 Elements of Monopole Dynamics90

9.7 Monopoles in Diagonalization Gauges91

10 Conclusions93

Aspects of BRST Quantization&J.W.van Holten99

1 Symmetries and Constraints99

1.1 Dynamical Systems with Constraints100

1.2 Symmetries and Noether's Theorems105

1.3 Canonical Formalism109

1.4 Quantum Dynamics113

1.5 The Relativistic Particle115

1.6 The Electro-magnetic Field119

1.7 Yang-Mills Theory121

1.8 The Relativistic String124

2 Canonical BRST Construction126

2.1 Grassmann Variables127

2.2 Classical BRST Transformations130

2.3 Examples133

2.4 Quantum BRST Cohomology135

2.5 BRST-Hodge Decomposition of States138

2.6 BRST Operator Cohomology142

2.7 Lie-Algebra Cohomology143

3 Action Formalism146

3.1 BRST Invariance from Hamilton's Principle146

3.2 Examples147

3.3 Lagrangean BRST Formalism148

3.4 The Master Equation152

3.5 Path-Integral Quantization154

4 Applications of BRST Methods156

4.1 BRST Field Theory156

4.2 Anomalies and BRST Cohomology158

Appendix Conventions165

Chiral Anomalies and Topology&J.Zinn-Justin167

1 Symmetries,Regularization,Anomalies167

2 Momentum Cut-Off Regularization170

2.1 Matter Fields：Propagator Modification170

2.2 Regulator Fields173

2.3 Abelian Gauge Theory174

2.4 Non-Abelian Gauge Theories177

3 Other Regularization Schemes178

3.1 Dimensional Regularization179

3.2 Lattice Regularization180

3.3 Boson Field Theories181

3.4 Fermions and the Doubling Problem182

4 The Abelian Anomaly184

4.1 Abelian Axial Current and Abelian Vector Gauge Fields184

4.2 Explicit Calculation188

4.3 Two Dimensions194

4.4 Non-Abelian Vector Gauge Fields and Abelian Axial Current195

4.5 Anomaly and Eigenvalues of the Dirac Operator196

5 Instantons,Anomalies,and 0-Vacua198

5.1 The Periodic Cosine Potential199

5.2 Instantons and Anomaly：CP(N-1) Models201

5.3 Instantons and Anomaly：Non-Abelian Gauge Theories206

5.4 Fermions in an Instanton Background210

6 Non-Abelian Anomaly212

6.1 General Axial Current212

6.2 Obstruction to Gauge Invariance214

6.3Wess-Zumino Consistency Conditions215

7 Lattice Fermions：Ginsparg-Wilson Relation216

7.1 Chiral Symmetry and Index217

7.2 Explicit Construction：Overlap Fermions221

8 Supersymmetric Quantum Mechanics and Domain Wall Fermions222

8.1 Supersymmetric Quantum Mechanics222

8.2 Field Theory in Two Dimensions226

8.3 Domain Wall Fermions227

Appendix A．Trace Formula for Periodic Potentials229

Appendix B．Resolvent of the Hamiltonian in Supersymmetric QM231

Supersymmetric Solitons and Topology&M.Shifman237

1 Introduction237

2 D=1+1;N=1238

2.1 Critical(BPS)Kinks242

2.2 The Kink Mass(Classical)243

2.3 Interpretation of the BPS Equations Morse Theory244

2.4 Quantization.Zero Modes：Bosonic and Fermionic245

2.5 Cancelation of Nonzero Modes248

2.6 Anomaly Ⅰ250

2.7 Anomaly Ⅱ(Shortening Supermultiplet Down to One State)252

3 Domain Walls in(3+1)-Dimensional Theories254

3.1 Superspace and Superfields254

3.2 Wess-Zumino Models256

3.3 Critical Domain Walls258

3.4 Finding the Solution to the BPS Equation261

3.5 Does the BPS Equation Follow from the Second Order Equation of Motion?261

3.6 Living on a Wall262

4 Extended Supersymmetry in Two Dimensions：The Supersymmetric CP(1) Model263

4.1 Twisted Mass266

4.2 BPS Solitons at the Classical Level267

4.3 Quantization of the Bosonic Moduli269

4.4 The Soliton Mass and Holomorphy271

4.5 Switching On Fermions273

4.6 Combining Bosonic and Fermionic Moduli274

5 Conclusions275

Appendix A．CP(1)Model=O(3)Model(N=1 Superfields N)275

Appendix B．Getting Started(Supersymmetry for Beginners)277

B.1 Promises of Supersymmetry280

B.2 Cosmological Term281

B.3 Hierarchy Problem281

Forces from Connes'Geometry&T.Schücker285

1 Introduction285

2 Gravity from Riemannian Geometry287

2.1 First Stroke：Kinematics287

2.2 Second Stroke：Dynamics287

3 Slot Machines and the Standard Model289

3.1 Input290

3.2 Rules292

3.3 The Winner296

3.4 Wick Rotation300

4 Connes'Noncommutative Geometry303

4.1 Motivation：Quantum Mechanics303

4.2 The Calibrating Example：Riemannian Spin Geometry305

4.3 Spin Groups308

5 The Spectral Action311

5.1 Repeating Einstein's Derivation in the Commutative Case311

5.2 Almost Commutative Geometry314

5.3 The Minimax Example317

5.4 A Central Extension322

6 Connes'Do-It-Yourself Kit323

6.1 Input323

6.2 Output327

6.3 The Standard Model329

6.4 Beyond the Standard Model337

7 Outlook and Conclusion338

Appendix340

A.1 Groups340

A.2 Group Representations342

A.3 Semi-Direct Product and Poincaré Group344

A.4 Algebras344

Index351