Quantum field theory and critical phenomena
Author(s)
Bibliographic Information
Quantum field theory and critical phenomena
（The international series of monographs on physics, 77）（Oxford science publications）
Clarendon Press , Oxford University Press, 1989
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
Over the last twenty years quantum field theory has become not only the framework for the discussion of all fundamental interactions but gravity, but also that for the understanding of second-order phase transitions in statistics mechanics. This advanced text is based on graduate courses and summer schools given over a number of years by the author. It approaches the subject in terms of path and functional integrals. A Euclidean metric has been adopted and the language of partition and correlation functions is used. Renormalization and the renormalization group are discussed. A major part of the book is then devoted to critical phenomena before the book concludes with a discussion of the role of instantons in quantum field theory.
Table of Contents
- Algebraic preliminaries
- Euclidean path integrals in quantum mechanics
- stochastic differential equations - Langevin, Fokker-Planck equations
- functional integrals in field theory
- generating functionals of correlation functions, loopwise expansion
- divergences in pertubation 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 examples 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 dynamical equations
- Abelian gauge theories
- non Abelian gauge theories
- 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
- calculation of universal quantities
- the (phi squared) squared field theory in the large N limit
- ferromagnetic order at low temperature - the non linear sigma-model
- the 0 (2) non linear sigma-model
- critical dynamics
- field theory in a finite geometry - finite size scaling
- critical properties of gauge theories
- large momentum behaviour in field theory
- 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 summation problem
- the "phi to the fourth" field theory in dimension four
- fermions and large order behaviour
- multi-instantons in quantum mechanics.
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