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格点量子场导论2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

格点量子场导论
  • Smit，J.编 著
  • 出版社： 北京;西安：世界图书出版公司
  • ISBN：7506260131
  • 出版时间：2003
  • 标注页数：271页
  • 文件大小：42MB
  • 文件页数：283页
  • 主题词：

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图书目录

1 Introduction1

1.1 QED,QCD,and confinement1

1.2 Scalar field5

2 Path-integral and lattice regularization8

2.1 Path integral in quantum mechanics8

2.2 Regularization by discretization10

2.3 Analytic continuation to imaginary time12

2.4 Spectrum of the transfer operator13

2.5 Latticization of the scalar field15

2.6 Transfer operator for the scalar field18

2.7 Fourier transformation on the lattice20

2.8 Free scalar field22

2.9 Particle interpretation25

2.10 Back to real time26

2.11 Problems28

3 O(n)models32

3.1 Goldstone bosons32

3.2 O(n)models as spin models34

3.3 Phase diagram and critical line36

3.4 Weak-coupling expansion39

3.5 Renormalization46

3.6 Renormalization-group beta functions48

3.7 Hopping expansion51

3.8 Lüscher-Weisz solution55

3.9 Numerical simulation60

3.10 Real-space renormalization group and universality67

3.11 Universality at weak coupling71

3.12 Triviality and the Standard Model74

3.13 Problems79

4 Gauge field on the lattice83

4.1 QED action83

4.2 QCD action85

4.3 Lattice gauge field90

4.4 Gauge-invariant lattice path integral95

4.5 Compact and non-compact Abelian gauge theory97

4.6 Hilbert space and transfer operator99

4.7 The kinetic-energy operator102

4.8 Hamiltonian for continuous time105

4.9 Wilson loop and Polyakov line107

4.10 Problems112

5 U(1)and SU(n) gauge theory115

5.1 Potential at weak coupling115

5.2 Asymptotic freedom121

5.3 Strong-coupling expansion125

5.4 Potential at strong coupling129

5.5 Confinement versus screening132

5.6 Glueballs135

5.7 Coulomb phase,confinement phase136

5.8 Mechanisms of confinement138

5.9 Scaling and asymptotic scaling,numerical results140

5.10 Problems144

6 Fermions on the lattice149

6.1 Naive discretization of the Dirac action149

6.2 Species doubling151

6.3 Wilson's fermion method156

6.4 Staggered fermions160

6.5 Transfer operator for Wilson fermions161

6.6 Problems165

7 Low-mass hadrons in QCD170

7.1 Integrating over the fermion fields170

7.2 Hopping expansion for the fermion propagator171

7.3 Meson and baryon propagators173

7.4 Hadron masses at strong coupling177

7.5 Numerical results179

7.6 The parameters of QCD188

7.7 Computing the gauge coupling from the masses190

7.8 Problems190

8 Chiral symmetry193

8.1 Chiral symmetry and effective action in QCD193

8.2 Pseudoscalar masses and the U(1) problem199

8.3 Chiral anomalies202

8.4 Chiral symmetry and the lattice204

8.5 Spontaneous breaking of chiral symmetry212

8.6 Chiral gauge theory217

8.7 Outlook223

8.8 Problems223

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 gauge239

Appendix C Fermionic coherent states242

Appendix D Spinor fields253

Notes258

References261

Index267

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