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Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamics has been the first example of a Quantum Field Theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics.
As this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale.
Therefore, this text sets out to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group properties are systematically discussed. The notion of effective field theory and the emergence of renormalisable theories are described. The consequences for fine tuning and triviality issue are emphasized.
This fifth edition has been updated and fully revised, e.g. in particle physics with progress in neutrino physics and the discovery of the Higgs boson. The presentation has been made more homogeneous througout the volume, and emphasis has been put on the notion of effective field theory and discussion of the emergence of renormalisable theories.
Sommario
- Preface
- 1: Gaussian integrals. Algebraic preliminaries
- 2: Euclidean path integrals and quantum mechanics
- 3: Quantum mechanics: Path integrals in phase space
- 4: Quantum statistical physics: Functional integration formalism
- 5: Quantum evolution: From particles to fields
- 6: The neutral relativistic scalar field
- 7: Perturbative quantum field theory: Algebraic methods
- 8: Ultraviolet divergences: Effective quantum field theory
- 9: Introduction to renormalization theory and renormalization group
- 10: Dimensional continuation, regularization. Minimal subtraction, RG functions
- 11: Renormalization of local polynomials. Short distance expansion
- 12: Relativistic fermions: Introduction
- 13: Symmetries, chiral symmetry breaking and renormalization
- 14: Critical phenomena: General considerations. Mean-field theory
- 15: The renormalization group approach: The critical theory near dimension 4
- 16: Critical domain: Universality, "-expansion
- 17: Critical phenomena: Corrections to scaling behaviour
- 18: O(N)-symmetric vector models for N large
- 19: The non-linear ?-model near two dimensions: Phase structure
- 20: Gross-Neveu-Yukawa and Gross-Neveu models
- 21: Abelian gauge theories: The framework of quantum electrodynamics
- 22: Non-Abelian gauge theories: Introduction
- 23: The Standard Model of fundamental interactions
- 24: Large momentum behaviour in quantum field theory
- 25: Lattice gauge theories: Introduction
- 26: BRST symmetry, gauge theories: Zinn-Justin equation and renormalization
- 27: Supersymmetric quantum field theory: Introduction
- 28: Elements of classical and quantum gravity
- 29: Generalized non-linear ?-models in two dimensions
- 30: A few two-dimensional solvable quantum field theories
- 31: O(2) spin model and Kosterlitz-Thouless's phase transition
- 32: Finite-size effects in field theory. Scaling behaviour
- 33: Quantum field theory at finite temperature: Equilibrium properties
- 34: Stochastic differential equations: Langevin, Fokker-Planck equations
- 35: Langevin field equations, properties and renormalization
- 36: Critical dynamics and renormalization group
- 37: Instantons in quantum mechanics
- 38: Metastable vacua in quantum field theory
- 39: Degenerate classical minima and instantons
- 40: Perturbative expansion at large orders
- 41: Critical exponents and equation of state from series summation
- 42: Multi-instantons in quantum mechanics
- Bibliography
- Index
Info autore
Jean Zinn-Justin, Scientific Advisor, CEA, Paris-Saclay. Jean Zinn-Justin has worked as a theoretical and mathematical physicist at Saclay Nuclear Research Centre (CEA) since 1965, where he was also Head of the Institute of Theoretical Physics from 1993-1998. Since 2010 he has also held the position of Adjunct Professor at Shanghai University. Previously he has served as a visiting professor at the Massachusetts Institute of Technology (MIT), Princeton University, State University of New York at Stony Brook, and Harvard University. He directed the Les Houches Summer School for theoretical physics from 1987 to 1995. He has served on editorial boards for several influential physics journals including the French Journal de Physique, Nuclear Physics B, Journal of Physics A, and the New Journal of Physics.
Riassunto
This work provides a systematic introduction to quantum field theory and renormalization group, as applied to particle physics and continuous macroscopic phase transitions.
Testo aggiuntivo
This excellent book offers a systematic presentation of the quantum field theory approach in describing all fundamental interactions in particle physics and the second order phase transition in statistical mechanics.
Relazione
Review from previous edition A remarkable achievement. I. D. Lawrie, Contemporary Physics
