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編輯推薦

　　相變無疑是物理學中的最重要的現象之一。對於相變的研究貫穿整個物理學，甚至是人類文明史。而現代物理學中，與相變息息相關的一個方法就是重正化群方法，其概念和思想已經滲透於物理學的各個領域。《中外物理學精品書係：相變與重正化群（英文影印版）》的引進，能夠供所有物理學領域的工作者作為參考。

內容簡介

　　《中外物理學精品書係：相變與重正化群（英文影印版）》詳細討論瞭相變與重正化群的關係。特彆是相變中的連續極限、相乾長度及標度律等等。本書適閤所有物理學領域的科研工作者和研究生閱讀。

作者簡介

　　（法）齊恩-硃斯坦，法國原子研究中心教授。

目錄

1 Quantum field theory and the renormalization group . . . . . . . . . 1
1.1 Quantum electrodynamics: A quantum field theory . . . . . . . . . 3
1.2 Quantum electrodynamics: The problem of infinities . . . . . . . . 4
1.3 Renormalization . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Quantum field theory and the renormalization group . . . . . . . . 9
1.5 A triumph of QFT: The Standard Model . . . . . . . . . . . . . 10
1.6 Critical phenomena: Other infinities . . . . . . . . . . . . . . . 12
1.7 Kadanoff and Wilson’s renormalizationgroup . . . . . . . . . . . 14
1.8 Effective quantum field theories . . . . . . . . . . . . . . . . . 16

2 Gaussian expectation values. Steepest descent method . . . . . . . . 19
2.1 Generating functions . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Gaussian expectation values.Wick’s theorem . . . . . . . . . . . 20
2.3 Perturbed Gaussian measure. Connected contributions . . . . . . . 24
2.4 Feynman diagrams. Connected contributions . . . . . . . . . . . . 25
2.5 Expectation values. Generating function. Cumulants . . . . . . . . 28
2.6 Steepest descent method . . . . . . . . . . . . . . . . . . . . 31
2.7 Steepest descent method: Several variables， generating functions . . . 37
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3 Universality and the continuum limit . . . . . . . . . . . . . . . . . 45
3.1 Central limit theorem of probabilities . . . . . . . . . . . . . . . 45
3.2 Universality and fixed points of transformations . . . . . . . . . . 54
3.3 Random walk and Brownian motion . . . . . . . . . . . . . . . 59
3.4 Random walk: Additional remarks . . . . . . . . . . . . . . . . 71
3.5 Brownian motion and path integrals . . . . . . . . . . . . . . . 72
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4 Classical statistical physics: One dimension . . . . . . . . . . . . . . 79
4.1 Nearest-neighbour interactions. Transfer matrix . . . . . . . . . . 80
4.2 Correlation functions . . . . . . . . . . . . . . . . . . . . . . 83
4.3 Thermodynamic limit . . . . . . . . . . . . . . . . . . . . . . 85
4.4 Connected functions and cluster properties . . . . . . . . . . . . 88
4.5 Statistical models: Simple examples . . . . . . . . . . . . . . . 90
4.6 The Gaussian model . . . . . . . . . . . . . . . . . . . . . . 924.7 Gaussian model: The continuumlimit . . . . . . . . . . . . . . . 98
4.8 More general models: The continuumlimit . . . . . . . . . . . 102
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5 Continuum limit and path integrals . . . . . . . . . . . . . . . . 111
5.1 Gaussian path integrals . . . . . . . . . . . . . . . . . . . . 111
5.2 Gaussian correlations.Wick’s theorem . . . . . . . . . . . . . 118
5.3 Perturbed Gaussian measure . . . . . . . . . . . . . . . . . . 118
5.4 Perturbative calculations: Examples . . . . . . . . . . . . . . 120
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

6 Ferromagnetic systems. Correlation functions . . . . . . . . . . . 127
6.1 Ferromagnetic systems: Definition . . . . . . . . . . . . . . . 127
6.2 Correlation functions. Fourier representation . . . . . . . . . . . 133
6.3 Legendre transformation and vertex functions . . . . . . . . . . 137
6.4 Legendre transformation and steepest descent method . . . . . . . 142
6.5 Two- and four-point vertex functions . . . . . . . . . . . . . . 143
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

7 Phase transitions: Generalities and examples . . . . . . . . . . . . 147
7.1 Infinite temperature or independent spins . . . . . . . . . . . . 150
7.2 Phase transitions in infinite dimension . . . . . . . . . . . . . 153
7.3 Universality in infinite space dimension . . . . . . . . . . . . . 158
7.4 Transformations， fixed points and universality . . . . . . . . . . 161
7.5 Finite-range interactions in finite dimension . . . . . . . . . . . 163
7.6 Ising model: Transfer matrix . . . . . . . . . . . . . . . . . . 166
7.7 Continuous symmetries and transfer matrix . . . . . . . . . . . 171
7.8 Continuous symmetries and Goldstone modes . . . . . . . . . . 173
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

8 Quasi-Gaussian approximation: Universality， critical dimension . . . . 179
8.1 Short-range two-spin interactions . . . . . . . . . . . . . . . . 181
8.2 The Gaussian model: Two-point function . . . . . . . . . . . . 183
8.3 Gaussian model and random walk . . . . . . . . . . . . . . . 188
8.4 Gaussian model and field integral . . . . . . . . . . . . . . . . 190
8.5 Quasi-Gaussian approximation . . . . . . . . . . . . . . . . . 194
8.6 The two-point function: Universality . . . . . . . . . . . . . . 196
8.7 Quasi-Gaussian approximation and Landau’s theory . . . . . . . 199
8.8 Continuous symmetries and Goldstone modes . . . . . . . . . . 200
8.9 Corrections to the quasi-Gaussian approximation . . . . . . . . . 202
8.10 Mean-field approximation and corrections . . . . . . . . . . . 207
8.11 Tricritical points . . . . . . . . . . . . . . . . . . . . . . 211
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

9 Renormalization group: General formulation . . . . . . . . . . . . 217
9.1 Statistical field theory. Landau’s Hamiltonian . . . . . . . . . . 218
9.2 Connected correlation functions. Vertex functions . . . . . . . . 220
9.3 Renormalization group: General idea . . . . . . . . . . . . . . 222
9.4 Hamiltonian flow: Fixed points， stability . . . . . . . . . . . . 226
9.5 The Gaussian fixed point . . . . . . . . . . . . . . . . . . . 2319.6 Eigen-perturbations: General analysis . . . . . . . . . . . . . . 234
9.7 A non-Gaussian fixed point: The ε-expansion . . . . . . . . . . 237
9.8 Eigenvalues and dimensions of local polynomials . . . . . . . . . 241

10 Perturbative renormalization group: Explicit calculations . . . . . . 243
10.1 Critical Hamiltonian and perturbative expansion . . . . . . . . 243
10.2 Feynman diagrams at one-loop order . . . . . . . . . . . . . . 246
10.3 Fixed point and critical behaviour . . . . . . . . . . . . . . . 248
10.4 Critical domain . . . . . . . . . . . . . . . . . . . . . . . 254
10.5 Models with O(N) orthogonal symmetry . . . . . . . . . . . . 258
10.6 Renormalization group near dimension 4 . . . . . . . . . . . . 259
10.7 Universal quantities: Numerical results . . . . . . . . . . . . . 262

11 Renormalization group: N-component fields . . . . . . . . . . . . 267
11.1 Renormalization group: General remarks . . . . . . . . . . . . 268
11.2 Gradient flow . . . . . . . . . . . . . . . . . . . . . . . . 269
11.3 Model with cubic anisotropy . . . . . . . . . . . . . . . . . 272
11.4 Explicit general expressions: RG analysis . . . . . . . . . . . . 276
11.5 Exercise: General model with two parameters . . . . . . . . . . 281
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

12 Statistical field theory: Perturbative expansion . . . . . . . . . . 285
12.1 Generating functionals . . . . . . . . . . . . . . . . . . . . 285
12.2 Gaussian field theory.Wick’s theorem . . . . . . . . . . . . . 287
12.3 Perturbative expansion . . . . . . . . . . . . . . . . . . . . 289
12.4 Loop expansion . . . . . . . . . . . . . . . . . . . . . . . 296
12.5 Dimensional continuation and regularization . . . . . . . . . . 299
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

13 The σ4 field theory near dimension 4 . . . . . . . . . . . . . . . 307
13.1 Effective Hamiltonian. Renormalization . . . . . . . . . . . . 308
13.2 Renormalization group equations . . . . . . . . . . . . . . . 313
13.3 Solution of RGE: The ε-expansion . . . . . . . . . . . . . . . 316
13.4 Effective and renormalized interactions . . . . . . . . . . . . . 323
13.5 The critical domain above Tc . . . . . . . . . . . . . . . . . 324

14 The O(N) symmetric (φ2)2 field theory in the large N limit . . . . 329
14.1 Algebraic preliminaries . . . . . . . . . . . . . . . . . . . . 330
14.2 Integration over the field φ: The determinant . . . . . . . . . . 331
14.3 The limit N →∞: The critic 中外物理學精品書係：相變與重正化群（英文影印版） 下載 mobi epub pdf txt 電子書

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中外物理學精品書係：相變與重正化群（英文影印版）》詳細討論瞭相變與重正化群的關係。特彆是相變中的連續極限、相乾長度及標度律等等。本書適閤所有物理學領域的科研工作者和研究生閱讀。

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