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Quantum Field Theory and Critical Phenomena

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ISBN-10: 0198509235

ISBN-13: 9780198509233

Edition: 4th 2002 (Revised)

Authors: Jean Zinn-Justin

List price: $150.00
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Description:

The book is an introduction to quantum field theory and renormalization group.It shows that these frameworks are essential for the understanding of phenomena belonging to many different areas of physics, which range from phase transitions in macroscopic systems to the theory of fundamental interactions. This advanced new edition is based on graduate courses and summer schools given by the author over a number of years. Although there are several good textbooks on QFT, this is thefirst to emphasize the common aspects of particle physics and the theory of critical phenomena in a unified framework. The book has been fully updated, with about 50% new material added. Three new chapters have been included: an introduction to non-relativistic quantum statistical physics; a chapter oncritical phenomena in non-magnetic systems, polymers, liquid-vapour, and helium superfluid transitions; and a chaper on finite temperature relativistic quantum field theory. The book can be roughly divided into four parts: chapters 1-12 deal with general field theory, functional integrals, and functional methods. In chapters 13-21, renormalization properties of theories with symmetries are studied and specific applications to particle physics are emphasized. Chapters 23-37 are devoted tocritical phenomena. Chapters 39-43 describe the role of instantons in quantum mechanics and field theory. Exercises that were originally included in previous editions will be supplied online at www-spht.ceafr/articles/T02/001.
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Book details

List price: $150.00
Edition: 4th
Copyright year: 2002
Publisher: Oxford University Press, Incorporated
Publication date: 8/15/2002
Binding: Hardcover
Pages: 1074
Size: 6.61" wide x 9.45" long x 2.35" tall
Weight: 3.872

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 of correlation functions: loopwise expansion
Divergencies 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
Calculation of universal quantities
The (O2)2 field theory in large N limit
Ferromagnetic order at low temperature: the non-linear sigma -model
A few two-dimensional models: Bosonization technique
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 O4 field theory in dimension four
Fermions and large order behaviour
Multi instantons in quantum mechanics
Index