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出版社:北京大學
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ISBN:9787301251850
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作者:(法)齊恩-朱斯坦
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頁數:454
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出版日期:2014-12-01
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印刷日期:2014-12-01
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包裝:平裝
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開本:16開
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版次:1
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印次:1
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字數:562千字
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相變無疑是物理學中的最重要的現像之一。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。本書的引進,能夠供所有物理學領域的工作者作 為參考。齊恩-朱斯坦編著的《相變與重正化群(影印 版)》詳細討論了相變與重正化群的關繫。特別是相 變中的連續極限、相干長度及標度律等等。本書適合 所有物理學領域的科研工作者和研究生閱讀。
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1 Quantum field theory and the renormalization group. 1.1 Quantum electrodynamics: A quantum field theory. 1.2 Quantum electrodynamics: The problem of infinities 1.3 Renormalization. 1.4 Quantum field theory and the renormalization group 1.5 A triumph of QFT: The Standard Model 1.6 Critical phenomena: Other infinities 1.7 Kadanoff and Wilson’s renormalizationgroup 1.8 Effective quantum field theories 2 Gaussian expectation values. Steepest descent method 2.1 Generating functions 2.2 Gaussian expectation values.Wick’s theorem 2.3 Perturbed Gaussian measure. Connected contributions 2.4 Feynman diagrams. Connected contributions. 2.5 Expectation values. Generating function. Cumulants 2.6 Steepest descent method 2.7 Steepest descent method: Several variables, generating functions Exercises 3 Universality and the continuum limit 3.1 Central limit theorem of probabilities 3.2 Universality and fixed points of transformations 3.3 Random walk and Brownian motion 3.4 Random walk: Additional remarks 3.5 Brownian motion and path integrals Exercises 4 Classical statistical physics: One dimension 4.1 Nearest-neighbour interactions. Transfer matrix 4.2 Correlation functions 4.3 Thermodynamic limit 4.4 Connected functions and cluster properties 4.5 Statistical models: Simple examples 4.6 The Gaussian model924.7 Gaussian model: The continuumlimit 4.8 More general models: The continuumlimit Exercises 5 Continuum limit and path integrals 5.1 Gaussian path integrals 5.2 Gaussian correlations.Wick’s theorem 5.3 Perturbed Gaussian measure 5.4 Perturbative calculations: Examples Exercises 6 Ferromagic systems. Correlation functions 6.1 Ferromagic systems: Definition 6.2 Correlation functions. Fourier representation 6.3 Legendre transformation and vertex functions 6.4 Legendre transformation and steepest descent method 6.5 Two- and four-point vertex functions Exercises145 7 Phase transitions: Generalities and examples 7.1 Infinite temperature or independent spins 7.2 Phase transitions in infinite dimension 7.3 Universality in infinite space dimension 7.4 Transformations, fixed points and universality 7.5 Finite-range interactions in finite dimension 7.6 Ising model: Transfer matrix 7.7 Continuous symmetries and transfer matrix 7.8 Continuous symmetries and Goldstone modes Exercises 8 Quasi-Gaussian approximation: Universality, critical dimension. 8.1 Short-range two-spin interactions 8.2 The Gaussian model: Two-point function. 8.3 Gaussian model and random walk 8.4 Gaussian model and field integral 8.5 Quasi-Gaussian approximation 8.6 The two-point function: Universality 8.7 Quasi-Gaussian approximation and Landau’s theory 8.8 Continuous symmetries and Goldstone modes 8.9 Corrections to the quasi-Gaussian approximation 8.10 Mean-field approximation and corrections 8.11 Tricritical points Exercises 9 Renormalization group: General formulation 9.1 Statistical field theory. Landau’s Hamiltonian 9.2 Connected correlation functions. Vertex functions 9.3 Renormalization group: General idea 9.4 Hamiltonian flow: Fixed points, stability 9.5 The Gaussian fixed point.2319.6 Eigen-perturbations: General analysis 9.7 A non-Gaussian fixed point: The ε-expansion 9.8 Eigenvalues and dimensions of local polynomials 10 Perturbative renormalization group: Explicit calculations. 10.1 Critical Hamiltonian and perturbative expansion 10.2 Feynman diagrams at one-loop order 10.3 Fixed point and critical behaviour 10.4 Critical domain 10.5 Models with O(N) orthogonal symmetry 10.6 Renormalization group near dimension 4 10.7 Universal quantities: Numerical results 11 Renormalization group: N-ponent fields 11.1 Renormalization group: General remarks 11.2 Gradient flow 11.3 Model with cubic anisotropy 11.4 Explicit general expressions: RG analysis 11.5 Exercise: General model with two parameters Exercises 12 Statistical field theory: Perturbative expansion 12.1 Generating functionals 12.2 Gaussian field theory.Wick’s theorem 12.3 Perturbative expansion 12.4 Loop expansion 12.5 Dimensional continuation and regularization Exercises 13 The σ4 field theory near dimension 4 13.1 Effective Hamiltonian. Renormalization 13.2 Renormalization group equations 13.3 Solution of RGE: The ε-expansion 13.4 Effective and renormalized interactions 13.5 The critical domain above Tc 14 The O(N) symmetric (φ2)2 field theory in the large N limit 14.1 Algebraic preliminaries 14.2 Integration over the field φ: The determinant 14.3 The limit N →∞: The critical domain 14.4 The (φ2)2 field theory for N →∞ 14.5 Singular part of the free energy and equation of state 14.6 The λλ and φ2φ2 two-point functions 14.7 Renormalization group and corrections to scaling 14.8 The 1/N expansion 14.9 The exponent η at order 1/N 14.10 The non-linear σ-model 15 The non-linear σ-model 15.1 The non-linear σ-model on the lattice 15.2 Low-temperature expansion 15.3 Formal continuum limit 15.4 Regularization 15.5 Zero-momentum or IR divergences 15.6 Renormalization group 15.7 Solution of the RGE. Fixed points 15.8 Correlation functions: Scaling form 15.9 The critical domain: Critical exponents 15.10 Dimension 2 15.11 The (φ2)2 field theory at low temperature 16 Functional renormalization group 16.1 Partial field integration and effective Hamiltonian 16.2 High-momentum mode integration andRGE 16.3 Perturbative solution: φ4 theory 16.4 RGE: Standard form 16.5 Dimension 4 16.6 Fixed point: ε-expansion 16.7 Local stability of the fixed point Appendix A1 Technical results A2 Fourier transformation: Decay and regularity A3 Phase transitions: General remarks A4 1/N expansion: Calculations A5 Functional renormalization group: Complements Bibliography Index
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