格点量子场导论PDF电子书下载

1 Introduction 1

1.1 QED,QCD,and confinement 1

1.2 Scalar field 5

2 Path-integral and lattice regularization 8

2.1 Path integral in quantum mechanics 8

2.2 Regularization by discretization 10

2.3 Analytic continuation to imaginary time 12

2.4 Spectrum of the transfer operator 13

2.5 Latticization of the scalar field 15

2.6 Transfer operator for the scalar field 18

2.7 Fourier transformation on the lattice 20

2.8 Free scalar field 22

2.9 Particle interpretation 25

2.10 Back to real time 26

2.11 Problems 28

3 O(n)models 32

3.1 Goldstone bosons 32

3.2 O(n)models as spin models 34

3.3 Phase diagram and critical line 36

3.4 Weak-coupling expansion 39

3.5 Renormalization 46

3.6 Renormalization-group beta functions 48

3.7 Hopping expansion 51

3.8 Lüscher-Weisz solution 55

3.9 Numerical simulation 60

3.10 Real-space renormalization group and universality 67

3.11 Universality at weak coupling 71

3.12 Triviality and the Standard Model 74

3.13 Problems 79

4 Gauge field on the lattice 83

4.1 QED action 83

4.2 QCD action 85

4.3 Lattice gauge field 90

4.4 Gauge-invariant lattice path integral 95

4.5 Compact and non-compact Abelian gauge theory 97

4.6 Hilbert space and transfer operator 99

4.7 The kinetic-energy operator 102

4.8 Hamiltonian for continuous time 105

4.9 Wilson loop and Polyakov line 107

4.10 Problems 112

5 U(1)and SU(n) gauge theory 115

5.1 Potential at weak coupling 115

5.2 Asymptotic freedom 121

5.3 Strong-coupling expansion 125

5.4 Potential at strong coupling 129

5.5 Confinement versus screening 132

5.6 Glueballs 135

5.7 Coulomb phase,confinement phase 136

5.8 Mechanisms of confinement 138

5.9 Scaling and asymptotic scaling,numerical results 140

5.10 Problems 144

6 Fermions on the lattice 149

6.1 Naive discretization of the Dirac action 149

6.2 Species doubling 151

6.3 Wilson's fermion method 156

6.4 Staggered fermions 160

6.5 Transfer operator for Wilson fermions 161

6.6 Problems 165

7 Low-mass hadrons in QCD 170

7.1 Integrating over the fermion fields 170

7.2 Hopping expansion for the fermion propagator 171

7.3 Meson and baryon propagators 173

7.4 Hadron masses at strong coupling 177

7.5 Numerical results 179

7.6 The parameters of QCD 188

7.7 Computing the gauge coupling from the masses 190

7.8 Problems 190

8 Chiral symmetry 193

8.1 Chiral symmetry and effective action in QCD 193

8.2 Pseudoscalar masses and the U(1) problem 199

8.3 Chiral anomalies 202

8.4 Chiral symmetry and the lattice 204

8.5 Spontaneous breaking of chiral symmetry 212

8.6 Chiral gauge theory 217

8.7 Outlook 223

8.8 Problems 223

Appendix A SU(n) 229

A.1 Fundamental representation of SU(n) 229

A.2 Adjoint representation of SU(n) 231

A.3 Left and right translations in SU(n) 234

A.4 Tensor method for SU(n) 236

Appendix B Quantization in the temporal gauge 239

Appendix C Fermionic coherent states 242

Appendix D Spinor fields 253

Notes 258

References 261

Index 267