From Brownian motion to renormalization and lattice gauge theory

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From Brownian motion to renormalization and lattice gauge theory / Claude Itzykson, Jean-Michel Drouffe

資料種別:

図書

出版情報:

Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1989

形態:

xvi, 403 p. ; 24 cm

シリーズ名:

Cambridge monographs on mathematical physics ; . Statistical field theory / Claude Itzykson, Jean-Michel Drouffe ; v. 1 <BA00074521>

著者名:

ISBN:

9780521340588 [0521340586] (: hc)

書誌ID:

BA07626590

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographies and index

主題:

Field theory (Physics); Statistical physics

言語:

英語

目次情報:

Contents of Volume 2

Preface

From Brownian motion to Euclidean fields / 1：

Brownian motion / 1.1：

Random walks / 1.1.1：

The sum over paths / 1.1.2：

The dimension two of Brownian curves / 1.1.3：

Euclidean fields / 1.2：

Free fields / 1.2.1：

Interacting fields and random walks / 1.2.2：

Self-avoiding walks and the limit n [right arrow] 0 / 1.2.3：

Comparison with the high temperature expansion / 1.2.4：

The one-dimensional case / 1.2.5：

Lattices / 1.A：

Notes

Grassmannian integrals and the two-dimensional Ising model / 2：

Grassmannian integrals / 2.1：

Anticommuting variables / 2.1.1：

Integrals / 2.1.2：

The two-dimensional Ising model / 2.2：

Duality / 2.2.1：

Transfer matrix / 2.2.2：

Fermionic representation / 2.2.3：

Free energy / 2.2.4：

Spontaneous magnetization / 2.2.5：

Correlation function in the high temperature phase / 2.2.6：

Surface tension / 2.2.7：

Critical continuous theory / 2.3：

Effective action / 2.3.1：

Correlation functions / 2.3.2：

Quadratic differences and Painleve equations / 2.A：

Spontaneous symmetry breaking, mean field / 3：

Mean field approximation / 3.1：

Dielectric constant of a polarizable medium / 3.1.1：

Classical spin model with a finite symmetry group / 3.1.2：

Continuous symmetry group / 3.1.3：

The Bethe approximation / 3.1.4：

Critical exponents / 3.1.5：

Lee-Yang zeroes / 3.2：

The Lee-Yang theorem / 3.2.1：

General properties / 3.2.2：

Zeroes in the temperature plane / 3.2.4：

Large n limit / 3.3：

Saddle point method / 3.3.1：

Factorization / 3.3.2：

Coupling to an external field / 3.3.3：

Corrections to mean field / 3.4：

Laplace transform / 3.4.1：

Scaling transformations and the XY-model / 4：

Scaling laws. Real space renormalization / 4.1：

Homogeneity and scale invariance / 4.1.1：

Recurrence relations in real space / 4.1.2：

Examples and approximations / 4.1.3：

The XY-model / 4.2：

High temperature behaviour / 4.2.1：

Low temperature expansion. Vortices / 4.2.2：

The Villain action / 4.2.3：

Correlations / 4.2.4：

Renormalization flow / 4.2.5：

Two-dimensional systems with continuous symmetry / 4.A：

Magnetization inequality / 4.A.1：

Correlation inequality / 4.A.2：

Phenomenological renormalization / 4.B：

Continuous field theory and the renormalization group / 5：

The Lagrangian and dimensional analysis / 5.1：

Introduction / 5.1.1：

Generating functionals and dimensional analysis / 5.1.2：

The perturbative method / 5.2：

Diagrammatic series / 5.2.1：

Loop expansion / 5.2.2：

Evaluation of integrals and dimensional continuation / 5.2.3：

Group theoretical factors / 5.2.4：

Power counting / 5.2.5：

Perturbative renormalization / 5.2.6：

The renormalization group / 5.3：

From the Gaussian ultraviolet fixed point to the infrared critical point in dimension less than four / 5.3.1：

Correlation functions at the critical point / 5.3.4：

Expansion near the critical point / 5.3.5：

Scaling laws below the critical temperature / 5.3.6：

Corrections to scaling laws / 5.4：

Deviation from the critical point in dimension lower than four / 5.4.1：

Logarithmic corrections in dimension four / 5.4.2：

Irrelevant operators / 5.4.3：

Numerical results / 5.5：

[varepsilon]-expansion of critical exponents / 5.5.1：

Equation of state / 5.5.2：

Amplitude ratios / 5.5.3：

Three-dimensional results / 5.5.4：

Multicritical points / 5.A：

Lattice gauge fields / 6：

Generalities / 6.1：

Presentation / 6.1.1：

The continuous limit / 6.1.2：

Order parameter and Elitzur's theorem / 6.1.3：

Structure of the phase diagram / 6.1.4：

Corrections to mean field and restoration of gauge invariance / 6.2.1：

Discrete groups: 1/d expansion / 6.2.3：

Continuous groups: computation of corrections / 6.2.4：

Strong coupling expansions / 6.3：

Convergence / 6.3.1：

Character expansions / 6.3.2：

String tension and roughening transition / 6.3.3：

Mass spectrum / 6.3.5：

Lattice fermions / 6.4：

The doubling problem / 6.4.1：

The Nielsen-Ninomiya theorem / 6.4.2：

Staggered fermions / 6.4.3：

Index

Grassmannian integrals and two-dimensional Ising models

Spontaneous symmetry breaking

Contents of Volume 2

Preface

From Brownian motion to Euclidean fields / 1：

Brownian motion / 1.1：

Random walks / 1.1.1：

The sum over paths / 1.1.2：

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