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基本説明
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 chapter 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.
Full 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 onQFT, 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 statisticalphysics; 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 23-37are 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.
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
