Quantum field theory and critical phenomena

書誌事項

Quantum field theory and critical phenomena

Jean Zinn-Justin

(The international series of monographs on physics, 92)(Oxford science publications)

Clarendon Press, 1996

3rd ed

大学図書館所蔵 件 / 66

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

Over the last twenty years quantum field theory has become not only the framework for the discussion of all fundamental interactions except gravity, but also for the understanding of second-order phase transitions in statistical mechanics. This advanced text is based on graduate courses and summer schools given by the author over a number of years. It approaches the subject in terms of path and functional intergrals, adopting a Euclidean metric and using the language of partition and correlation functions. Renormalization and the renormalization group are examined, as are critical phenomena and the role of instantons. Changes for this edition 1. Extensive revision to eliminate a few bugs that had survived the second edition and (mainly) to improve the pedagogical presentation, as a result of experience gathered by lecturing. 2. Additional new topics; holomorphic or coherent state path integral; functional integral and representation of the field theory S-matrix in the holomorphic formalis; non-relativistic limit of massive quantization and brief discussion of non-renormalization of quantum gravity based on Einstein action. 3. This book is intended for theoretical particle physicists and statistical physicists at graduate level and above.

目次

  • Algebraic preliminaries
  • Euclidean path integrals in quantum mechanics
  • Path integrals in quantum mechanics: generalizations
  • Stochastic differential equations: Langevin, Fokker Planck equations
  • Functional integrals in field theory
  • Generating functionals or correlation functions: loopwise expansion
  • Divergences in perturbation theory, power counting
  • Regularization methods
  • Introduction to renormalization theory, renormalization group equations
  • Dimensional regularization and minimal subtraction: calculation of RG functions
  • Renormalization of composite operators: short distance expansion: Linearly realized symmetries and renormalization
  • Non-linearly realized symmetries: the example of the non-linear sigma model
  • Models on homogeneous spaces in two dimensions
  • Symmetric spaces: non-local conservation laws, renormalization group
  • Slavnov Taylor and BRS symmetry: stochastic field equations
  • Renormalization and stochastic field equations: supersymmetry
  • Abelian gauge theory
  • Non-Abelian gauge theories: introduction: The standard model: anomalies
  • Renormalization of gauge theories: general formalism
  • Critical phenomena: general considerations
  • Mean field theory for ferromagnetic systems: General renormalization group analysis: the critical theory near dimension four
  • Scaling behaviour in the critical domain
  • Corrections to scaling behaviour
  • Calculations of universal quantities
  • The field theory in large N limit
  • Ferromagnetic order at low temperature: the non-linear sigma model
  • A few two-dimensional models: Bosonization technique: The O(2) Non-linear sigma model
  • Critical properties of gauge theories
  • Large momentum behaviour in field theory
  • Critical dynamics
  • Field theory in a finite geometry: finite size scaling
  • Instantons in quantum mechanics: the anharmonic oscillator
  • Quantum mechanics: generalization
  • Unstable vacua in field theory
  • Degenerate classical minima and instantons
  • Perturbation theory at large orders and instantons
  • The field theory in dimension four
  • Fermions and large order behaviour
  • Multi-instantons in quantum mechanics.

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