相变与重正化群=PHASE TRANSITIONS AND RENORMALIZATION GROUP 影印版 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

相变与重正化群=PHASE TRANSITIONS AND RENORMALIZATION GROUP 影印版 英文PDF格式电子书版下载

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1 Quantum field theory and the renormalization group1

1.1 Quantum electrodynamics：A quantum field theory3

1.2 Quantum electrodynamics：The problem of infinities4

1.3 Renormalization7

1.4 Quantum field theory and the renormalization group9

1.5 A triumph of QFT：The Standard Model10

1.6 Critical phenomena：Other infinities12

1.7 Kadanoff and Wilson's renormalization group14

1.8 Effective quantum field theories16

2 Gaussian expectation values.Steepest descent method19

2.1 Generating functions19

2.2 Gaussian expectation values.Wick's theorem20

2.3 Perturbed Gaussian measure.Connected contributions24

2.4 Feynman diagrams.Connected contributions25

2.5 Expectation values.Generating function.Cumulants28

2.6 Steepest descent method31

2.7 Steepest descent method：Several variables,generating functions37

Exercises40

3 Universality and the continuum limit45

3.1 Central limit theorem of probabilities45

3.2 Universality and fixed points of transformations54

3.3 Random walk and Brownian motion59

3.4 Random walk：Additional remarks71

3.5 Brownian motion and path integrals72

Exercises75

4 Classical statistical physics：One dimension79

4.1 Nearest-neighbour interactions Transfer matrix80

4.2 Correlation functions83

4.3 Thermody namics limit85

4.4 Connected functions and cluster properties88

4.5 Statistical models：Simple examples90

4.6 The Gaussian model92

4.7 Gaussian model：The continuum limit98

4.8 More general models：The continuum limit102

Exercises104

5 Continuum limit and path integrals111

5.1 Gaussian path integrals111

5.2 Gaussian correlations.Wick's theorem118

5.3 Perturbed Gaussian measure118

5.4 Perturbative calculations：Examples120

Exercises124

6 Ferromagnetic systems.Correlation functions127

6.1 Ferromagnetic systems：Definition127

6.2 Correlation functions.Fourier representation133

6.3 Legendre transformation and vertex functions137

6.4 Legendre transformation and steepest descent method142

6.5 Two-and four-point vertex functions143

Exercises145

7 Phase transitions：Generalities and examples147

7.1 Infinite temperature or independent spins150

7.2 Phase transitions in infinite dimension153

7.3 Universality in infinite space dimension158

7.4 Transformations,fixed points and universality161

7.5 Finite-range interactions in finite dimension163

7.6 Ising model：Transfer matrix166

7.7 Continuous symmetries and transfer matrix171

7.8 Continuous symmetries and Goldstone modes173

Exercises175

8 Quasi-Gaussian approximation：Universality,critical dimension179

8.1 Short-range two-spin interactions181

8.2 The Gaussian model：Two-point function183

8.3 Gaussian model and random walk188

8.4 Gaussian model and field integral190

8.5 Quasi-Gaussian approximation194

8.6 The two-point function：Universality196

8.7 Quasi-Gaussian approximation and Landau's theory199

8.8 Continuous symmetries and Goldstone modes200

8.9 Corrections to the quasi-Gaussian approximation202

8.10 Mean-field approximation and corrections207

8.11 Tricritical points211

Exercises212

9 Renormalization group：General formulation217

9.1 Statistical field theory.Landau's Hamiltonian218

9.2 Connected correlation functions.Vertex functions220

9.3 Renormalization group(RG)：General idea222

9.4 Hamiltonian flow：Fixed points,stability226

9.5 The Gaussian fixed point231

9.6 Eigen-perturbations：General analysis234

9.7 A non-Gaussian fixed point：The ε-expansion237

9.8 Eigenvalues and dimensions of local polynomials241

10 Perturbative renormalization group：Explicit calculations243

10.1 Critical Hamiltonian and perturbative expansion243

10.2 Feynman diagrams at one-loop order246

10.3 Fixed point and critical behaviour248

10.4 Critical domain254

10.5 Models with O(N)orthogonal symmetry258

10.6 RG near dimension 4259

10.7 Universal quantities：Numerical results262

11 Renormalization group：N-component fields267

11.1 RG：General remarks268

11.2 Gradient flow269

11.3 Model with cubic anisotropy272

11.4 Explicit general expressions：RG analysis276

11.5 Exercise：General model with two parameters281

Exercises284

12 Statistical field theory：Perturbative expansion285

12.1 Generating functionals285

12.2 Gaussian field theory.Wick's theorem287

12.3 Perturbative expansion289

12.4 Loop expansion296

12.5 Dimensional continuation and dimensional regularization299

Exercises306

13 Theσ4 field theory near dimension 4307

13.1 Effective Hamiltonian.Renormalization308

13.2 RG equations313

13.3 Solution ofRG equations：Theε-expansion316

13.4 The critical domain above Tc322

13.5 RG equations for renormalized vertex functions326

13.6 Effective and renormalized interactions328

14 The O(N)symmetric(φ2)2 field theory in the large N limit331

14.1 Algebraic preliminaries332

14.2 Integration over the fieldφ：The determinant333

14.3 The limit N→∞：The critical domain337

14.4 The(φ2)2 field theory for N→∞339

14.5 Singular part of the free energy and equation of state342

14.6 The〈λλ〉and〈φ2φ2〉two-point functions345

14.7 RG and corrections to scaling347

14.8 The 1/N expansion350

14.9 The exponent ηat order 1/N352

14.10 The non-linearσ-model353

15 The non-linearσ-model355

15.1 The non-linearσ-model on the lattice355

15.2 Low-temperature expansion357

15.3 Formal continuum limit362

15.4 Regularization363

15.5 Zero-momentum or IR divergences364

15.6 Renormalization group365

15.7 Solution of the RGE.Fixed points370

15.8 Correlation functions：Scaling form372

15.9 The critical domain：Critical exponents374

15.10 Dimension 2375

15.11 The(φ2)2 field theory at low temperature379

16 Functional renormalization group383

16.1 Partial field integration and effective Hamiltonian383

16.2 High-momentum mode integration and RG equations392

16.3 Perturbative solution：φ4 theory398

16.4 RG equations：Standard form401

16.5 Dimension 4404

16.6 Fixed point：ε-expansion411

16.7 Local stability of the fixed point413

Appendix419

A1 Technical results419

A2 Fourier transformation：Decay and regularity423

A3 Phase transitions：General remarks428

A4 1/N expansion：Calculations433

A5 Functional flow equations：Additional considerations435

Bibliography443

Index449