Overview

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.

Full Product Details

Author:   Jean Zinn-Justin (Scientific adviser at CEA and Academy member, Scientific adviser at CEA and Academy member, IRFU/CEA, Paris-Saclay University)
Publisher:   Oxford University Press
Imprint:   Oxford University Press
Edition:   5th Revised edition
Volume:   171
Dimensions:   Width: 17.50cm , Height: 4.50cm , Length: 25.50cm
Weight:   1.762kg
ISBN:  

9780198834625

ISBN 10:   0198834624
Pages:   1088
Publication Date:   15 April 2021
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us.

Table of Contents

"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: GrossDSNeveuDSYukawa and GrossDSNeveu 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 KosterlitzDSThouless>'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, FokkerDSPlanck 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"

Reviews

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. * Giuseppe Mussardo, Mathematical Reviews * This excellent book is surely destined to become a valuable and standard work of reference. * Lewis Ryder, Times Higher Educational Supplement * Review from previous edition A remarkable achievement. * I. D. Lawrie, Contemporary Physics *

Author Information

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.

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