格点规范理论 第4版 英文

1．INTRODUCTION 1

2．THE PATH INTEGRAL APPROACH TO QUANTIZATION 7

2.1 The Path Integral Method in Quantum Mechanics 8

2.2 Path Integral Representation of Bosonic Green Functions in Field theory 15

2.3 The Transfer Matrix 22

2.4 Path Integral Representation of Fermionic Green Functions 23

2.5 Discretizing Space-Time.The Lattice as a Regulator of a Quantum Field Theory 33

3．THE FREE SCALAR FIELD ON THE LATTICE 36

4．FERMIONS ON THE LATTICE 43

4.1 The Doubling Problem 43

4.2 A Closer Look at Fermion Doubling 48

4.3 Wilson Fermions 56

4.4 Staggered Fermions 57

4.5 Technical Details of the Staggered Fermion Formulation 61

4.6 Staggered Fermions in Momentum Space 69

4.7 Ginsparg-Wilson Fermions.The Overlap Operator 73

5．ABELIAN GAUGE FIELDS ON THE LATTICE AND COMPACT QED 77

5.1 Preliminaries 77

5.2 Lattice Formulation of QED 80

6．NON ABELIAN GAUGE FIELDS ON THE LATTICE COMPACT QCD 87

7．THE WILSON LOOP AND THE STATIC QUARK-ANTIQUARK POTENTIAL 95

7.1 A Look at Non-Relativistic Quantum Mechanics 96

7.2 The Wilson Loop and the Static q？-Potential in QED 97

7.3 The Wilson Loop in QCD 105

8．THE Q？-POTENTIAL IN SOME SIMPLE MODELS 109

8.1 The Potential in Quenched QED 109

8.2 The Potential in Quenched Compact QED2 114

9．THE CONTINUUM LIMIT OF LATTICE QCD 119

9.1 Critical Behaviour of Lattice QCD and the Continuum Limit 119

9.2 Dependence of the Coupling Constant on the Lattice Spacing and the Renormalization Group β-Function 122

10．LATTICE SUM RULES 130

10.1 Energy Sum Rule for the Harmonic Oscillator 130

10.2 The SU（N） Gauge Action on an Anisotropic Lattice 136

10.3 Sum Rules for the Static q？-Potential 138

10.4 Determination of the Electric,Magnetic and Anomalous Contribution to the ？Potential 146

10.5 Sum Rules for the Glueball Mass 148

11．THE STRONG COUPLING EXPANSION 151

11.1 The q？-Potential to Leading Order in Strong Coupling 151

11.2 Beyond the Leading Approximation 154

11.3 The Lattice Hamiltonian in the Strong Coupling Limit and the String Picture of Confinement 158

12．THE HOPPING PARAMETER EXPANSION 170

12.1 Path Integral Representation of Correlation Functions in Terms of Bosonic Variables 171

12.2 Hopping Parameter Expansion of the Fermion Propagator in an External Field 174

12.3 Hopping Parameter Expansion of the Effective Action 179

12.4 The HPE and the Pauli Exclusion Principle 183

13．WEAK COUPLING EXPANSION（Ⅰ）.THE Ф3-THEORY 192

13.1 Introduction 192

13.2 Weak Coupling Expansion of Correlation Functions in the φ3-Theory 195

13.3 The Power Counting Theorem of Reisz 201

14．WEAK COUPLING EXPANSION（Ⅱ）.LATTICE QED 209

14.1 The Gauge Fixed Lattice Action 209

14.2 Lattice Feynman Rules 216

14.3 Renormalization of the Axial Vector Current in One-Loop Order 222

14.4 The ABJ Anomaly 234

15．WEAK COUPLING EXPANSION（Ⅲ）.LATTICE QCD 242

15.1 The Link Integration Measure 243

15.2 Gauge Fixing and the Faddeev-Popov Determinant 247

15.3 The Gauge Field Action 252

15.4 Propagators and Vertices 257

15.5 Relation between ∧L and the ∧-Parameter of Continuum QCD 272

15.6 Universality of the Axial Anomaly in Lattice QCD 275

16．MONTE CARLO METHODS 284

16.1 Introduction 284

16.2 Construction Principles for Algorithms.Markov Chains 286

16.3 The Metropolis Method 291

16.4 The Langevin Algorithm 293

16.5 The Moleeular Dynamics Method 295

16.6 The Hybrid Algorithm 301

16.7 The Hybrid Monte Carlo Algorithm 304

16.8 The Pseudofermion Method 307

16.9 Application of the Hybrid Monte Carlo Algorithm to Systems with Fermions 313

17．SOME RESULTS OF MONTE CARLO CALCULATIONS 317

17.1 The String Tension and the q？ Potential in the SU（3）Gauge Theory 317

17.2 The q？-Potential in Full QCD 324

17.3 Chiral Symmetry Breaking 326

17.4 Glueballs 330

17.5 Hadron Mass Spectrum 336

17.6 Instantons 345

17.7 Flux Tubes in q？and qqq-Systems 359

17.8 The Dual Superconductor Picture of Confinement 363

17.9 Center Vortices and Confinement 373

17.10 Calorons 382

18．PATH-INTEGRAL REPRESENTATON OF THE THERMODYNAMICAL PARTITION FUNCTION FOR SOME SOLVABLE BOSONIC AND FERMIONIC SYSTEMS 402

18.1 Introduction 402

18.2 Path-Integral Representation of the Partition Function in Quantum Mechanics 403

18.3 Sum Rule for the Mean Energy 405

18.4 Test of the Energy Sum Rule.The Harmonic Oscillator 408

18.5 The Free Relativistic Boson Gas in the Path Integral Approach 413

18.6 The Photon Gas in the Path Integral Approach 417

18.7 Functional Methods for Fermions.Basics 420

18.8 Path Integral Representation of the Partition Function for a Fermionic System valid for Arbitrary Time-Step 424

18.9 A Modified Fermion Action Leading to Fermion Doubling 429

18.10 The Free Dirac Gas.Continuum Approach 432

18.11 Dirac Gas of Wilson Fermions on the Lattice 436

19．FINITE TEMPERATURE PERTURBATION THEORY OFF AND ON THE LATTICE 443

19.1 Feynman Rules For Thermal Green Functions in the λφ4Theory 443

19.2 Generation of a Dynamical Mass at T≠0 452

19.3 Perturbative Expansion of the Thermodynamical Potential 453

19.4 Feynman Rules for QED and QCD at Non-Vanishing Temperature and Chemical Potential in the Continuum 459

19.5 Temporal Structure of the Fermion Propagator at T≠0 and μ≠0 in the Continuum 464

19.6 The Electric Screening Mass in Continuum QED in One-Loop Order 467

19.7 The Electric Screening Mass in Continuum QCD in One-Loop Order 471

19.8 Lattice Feynman Rules for QED and QCD at T≠0 and μ≠0 474

19.9 Particle-Antiparticle Spectrum of the Fermion Propagator at T≠0 andμ≠0.Naive vs.Wilson Fermions 479

19.10 The Electric Screening Mass for Wilson Fermions in Lattice QED to One-Loop Order 483

19.11 The Electric Screening Mass for Wilson Fermions in Lattice QCD to One-Loop Order 491

19.12 The Infrared Problem 501

20．NON-PERTURBATIVE QCD AT FINITE TEMPERATURE 504

20.1 Thermodynamics on the Lattice 504

20.2 The Wilson Line or Polyakov Loop 509

20.3 Spontaneous Breakdown of the Center Symmetry and the Deconfinement Phase Transition 514

20.4 How to Determine the Transition Temperature 515

20.5 A Two-Dimensional Model.Test of Theoretical Concepts 517

20.6 Monte Carlo Study of the Deconfinement Phase Transition in the Pure SU（3） Gauge Theory 531

20.7 The Chiral Phase Transition 539

20.8 Some Monte Carlo Results on the High Temperature Phase of QCD 543

20.9 Some Possible Signatures for Plasma Formation 551

Appendix A 561

Appendix B 571

Appendix C 573

Appendix D 576

Appendix E 579

Appendix F 581

Appendix G 583

References 590

Index 605