格点规范理论 第4版 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

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1．INTRODUCTION1

2．THE PATH INTEGRAL APPROACH TO QUANTIZATION7

2.1 The Path Integral Method in Quantum Mechanics8

2.2 Path Integral Representation of Bosonic Green Functions in Field theory15

2.3 The Transfer Matrix22

2.4 Path Integral Representation of Fermionic Green Functions23

2.5 Discretizing Space-Time.The Lattice as a Regulator of a Quantum Field Theory33

3．THE FREE SCALAR FIELD ON THE LATTICE36

4．FERMIONS ON THE LATTICE43

4.1 The Doubling Problem43

4.2 A Closer Look at Fermion Doubling48

4.3 Wilson Fermions56

4.4 Staggered Fermions57

4.5 Technical Details of the Staggered Fermion Formulation61

4.6 Staggered Fermions in Momentum Space69

4.7 Ginsparg-Wilson Fermions.The Overlap Operator73

5．ABELIAN GAUGE FIELDS ON THE LATTICE AND COMPACT QED77

5.1 Preliminaries77

5.2 Lattice Formulation of QED80

6．NON ABELIAN GAUGE FIELDS ON THE LATTICE COMPACT QCD87

7．THE WILSON LOOP AND THE STATIC QUARK-ANTIQUARK POTENTIAL95

7.1 A Look at Non-Relativistic Quantum Mechanics96

7.2 The Wilson Loop and the Static q？-Potential in QED97

7.3 The Wilson Loop in QCD105

8．THE Q？-POTENTIAL IN SOME SIMPLE MODELS109

8.1 The Potential in Quenched QED109

8.2 The Potential in Quenched Compact QED2114

9．THE CONTINUUM LIMIT OF LATTICE QCD119

9.1 Critical Behaviour of Lattice QCD and the Continuum Limit119

9.2 Dependence of the Coupling Constant on the Lattice Spacing and the Renormalization Group β-Function122

10．LATTICE SUM RULES130

10.1 Energy Sum Rule for the Harmonic Oscillator130

10.2 The SU（N） Gauge Action on an Anisotropic Lattice136

10.3 Sum Rules for the Static q？-Potential138

10.4 Determination of the Electric,Magnetic and Anomalous Contribution to the ？Potential146

10.5 Sum Rules for the Glueball Mass148

11．THE STRONG COUPLING EXPANSION151

11.1 The q？-Potential to Leading Order in Strong Coupling151

11.2 Beyond the Leading Approximation154

11.3 The Lattice Hamiltonian in the Strong Coupling Limit and the String Picture of Confinement158

12．THE HOPPING PARAMETER EXPANSION170

12.1 Path Integral Representation of Correlation Functions in Terms of Bosonic Variables171

12.2 Hopping Parameter Expansion of the Fermion Propagator in an External Field174

12.3 Hopping Parameter Expansion of the Effective Action179

12.4 The HPE and the Pauli Exclusion Principle183

13．WEAK COUPLING EXPANSION（Ⅰ）.THE Ф3-THEORY192

13.1 Introduction192

13.2 Weak Coupling Expansion of Correlation Functions in the φ3-Theory195

13.3 The Power Counting Theorem of Reisz201

14．WEAK COUPLING EXPANSION（Ⅱ）.LATTICE QED209

14.1 The Gauge Fixed Lattice Action209

14.2 Lattice Feynman Rules216

14.3 Renormalization of the Axial Vector Current in One-Loop Order222

14.4 The ABJ Anomaly234

15．WEAK COUPLING EXPANSION（Ⅲ）.LATTICE QCD242

15.1 The Link Integration Measure243

15.2 Gauge Fixing and the Faddeev-Popov Determinant247

15.3 The Gauge Field Action252

15.4 Propagators and Vertices257

15.5 Relation between ∧L and the ∧-Parameter of Continuum QCD272

15.6 Universality of the Axial Anomaly in Lattice QCD275

16．MONTE CARLO METHODS284

16.1 Introduction284

16.2 Construction Principles for Algorithms.Markov Chains286

16.3 The Metropolis Method291

16.4 The Langevin Algorithm293

16.5 The Moleeular Dynamics Method295

16.6 The Hybrid Algorithm301

16.7 The Hybrid Monte Carlo Algorithm304

16.8 The Pseudofermion Method307

16.9 Application of the Hybrid Monte Carlo Algorithm to Systems with Fermions313

17．SOME RESULTS OF MONTE CARLO CALCULATIONS317

17.1 The String Tension and the q？ Potential in the SU（3）Gauge Theory317

17.2 The q？-Potential in Full QCD324

17.3 Chiral Symmetry Breaking326

17.4 Glueballs330

17.5 Hadron Mass Spectrum336

17.6 Instantons345

17.7 Flux Tubes in q？and qqq-Systems359

17.8 The Dual Superconductor Picture of Confinement363

17.9 Center Vortices and Confinement373

17.10 Calorons382

18．PATH-INTEGRAL REPRESENTATON OF THE THERMODYNAMICAL PARTITION FUNCTION FOR SOME SOLVABLE BOSONIC AND FERMIONIC SYSTEMS402

18.1 Introduction402

18.2 Path-Integral Representation of the Partition Function in Quantum Mechanics403

18.3 Sum Rule for the Mean Energy405

18.4 Test of the Energy Sum Rule.The Harmonic Oscillator408

18.5 The Free Relativistic Boson Gas in the Path Integral Approach413

18.6 The Photon Gas in the Path Integral Approach417

18.7 Functional Methods for Fermions.Basics420

18.8 Path Integral Representation of the Partition Function for a Fermionic System valid for Arbitrary Time-Step424

18.9 A Modified Fermion Action Leading to Fermion Doubling429

18.10 The Free Dirac Gas.Continuum Approach432

18.11 Dirac Gas of Wilson Fermions on the Lattice436

19．FINITE TEMPERATURE PERTURBATION THEORY OFF AND ON THE LATTICE443

19.1 Feynman Rules For Thermal Green Functions in the λφ4Theory443

19.2 Generation of a Dynamical Mass at T≠0452

19.3 Perturbative Expansion of the Thermodynamical Potential453

19.4 Feynman Rules for QED and QCD at Non-Vanishing Temperature and Chemical Potential in the Continuum459

19.5 Temporal Structure of the Fermion Propagator at T≠0 and μ≠0 in the Continuum464

19.6 The Electric Screening Mass in Continuum QED in One-Loop Order467

19.7 The Electric Screening Mass in Continuum QCD in One-Loop Order471

19.8 Lattice Feynman Rules for QED and QCD at T≠0 and μ≠0474

19.9 Particle-Antiparticle Spectrum of the Fermion Propagator at T≠0 andμ≠0.Naive vs.Wilson Fermions479

19.10 The Electric Screening Mass for Wilson Fermions in Lattice QED to One-Loop Order483

19.11 The Electric Screening Mass for Wilson Fermions in Lattice QCD to One-Loop Order491

19.12 The Infrared Problem501

20．NON-PERTURBATIVE QCD AT FINITE TEMPERATURE504

20.1 Thermodynamics on the Lattice504

20.2 The Wilson Line or Polyakov Loop509

20.3 Spontaneous Breakdown of the Center Symmetry and the Deconfinement Phase Transition514

20.4 How to Determine the Transition Temperature515

20.5 A Two-Dimensional Model.Test of Theoretical Concepts517

20.6 Monte Carlo Study of the Deconfinement Phase Transition in the Pure SU（3） Gauge Theory531

20.7 The Chiral Phase Transition539

20.8 Some Monte Carlo Results on the High Temperature Phase of QCD543

20.9 Some Possible Signatures for Plasma Formation551

Appendix A561

Appendix B571

Appendix C573

Appendix D576

Appendix E579

Appendix F581

Appendix G583

References590

Index605