相变与重正化群-(影印版)
本书特色
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《相变与重正化群(英文影印版)》详细讨论了相变与重正化群的关系。特别是相变中的连续极限、相干长度及标度律等等。本书适合所有物理学领域的科研工作者和研究生阅读。
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内容简介
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相变无疑是物理学中的*重要的现象之一。对于相变的研究贯穿整个物理学，甚至是人类文明史。而现代物理学中，与相变息息相关的一个方法就是重正化群方法，其概念和思想已经渗透于物理学的各个领域。《相变与重正化群(英文影印版)》的引进，能够供所有物理学领域的工作者作为参考。
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目录
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 theories2 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 exercises3 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 exercises4 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 exercises5 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 exercises6 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 exercises1457 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 exercises8 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 exercises9 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 polynomials10 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 results11 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 exercises12 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 exercises13 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 tc14 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-model15 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 temperature16 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 pointappendix a1 technical results a2 fourier transformation: decay and regularity a3 phase transitions: general remarks a4 1/n expansion: calculations a5 functional renormalization group: complementsbibliographyindex
封面
书名:相变与重正化群-(影印版)
作者:齐恩-朱斯坦
页数:454
定价:¥80.0
出版社:北京大学出版社
出版日期:2014-12-01
ISBN:9787301251850
PDF电子书大小:128MB 高清扫描完整版