CiNii Books - Quantum field theory and critical phenomena

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 the first 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 on critical 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 to critical 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.

Table of Contents

1. Algebraic Preliminaries
2. Euclidean Path Integrals in Quantum Mechanics
3. Path Integrals in Quantum Mechanics: Generalizations
4. Stochastic Differential Equatons: Langevin, Fokker-Planck Equations
5. Path and Functional Integrals in Quantum Statistical Physics
6. Quantum Evolution: from Particles to Fields
7. Quantum Field Theory: Functional Methods. Perturbation Theory
8. Relativistic Fermions
9. Quantum Field Theory: Divergences and Regularization
10. Introduction to Renormalization Theory. Renormalization Group Equations
11. Dimensional Regularization, Minimal Subtraction: RG Functions
12. Renormalization of Composite Operators. Short Distance Expansion
13. Symmetries and Renormalization
14. The Non-Linear sigma-Model: An Example of a Non-Linear Symmetry
15. General Non-Linear Models in Two Dimensions
16. BRS Symmetry and Stochastic Field Equations
17. From Langevin Equation to Supersymmetry
18. Abelian Gauge Theories
19. Non-Abelian Gauge Theories: Introduction
20. The Standard Model. Anomalies
21. Gauge Theories: Master Equation and Renormalization
22. Classical and Quantum Gravity. Riemannian Manifolds and Tensors
23. Critical Phenomena: General Considerations
24. Mean Field Theory for Ferromagnetic Systems
25. General Renormalization Group. The Critical Theory Near Dimension Four
26. Scaling Behaviour in the Critical Domain
27. Corrections to Scaling Behaviour
28. Non-Magnetic Systems and the (phi squared)squared Field Theory (see TOC for exact title)
29. Calculation of Universal Quantities
30. The O(N) Vector Model for N Large
31. Phase Transitions Near Two Dimensions
32. Two-Dimensional Modes and Bosonization Method
33. The O(2) Classical Spin Model in Two Dimensions
34. Critical Properties of Gauge Theories
35. UV Fixed Points in Quantum Field Theory
36. Critical Dynamics
37. Field Theory in a Finite Geometry: Finite Size Scaling
38. Quantum Field Theory at Finite Temperature: Equilibrium Properties
39. Instantons in Quantum Mechanics
40. Unstable Vacua in Quantum Field Theory
41. Degenerate Classical Minima and Instantons
42. Perturbation Series at Large Orders. Summation Methods
43. Multi-Instantons in Quantum Mechanics

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Quantum field theory and critical phenomena

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