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.
This work provides a systematic introduction to quantum field theory and renormalization group, as applied to particle physics and continuous macroscopic phase transitions.
Arvustused
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 * A remarkable achievement. * I. D. Lawrie, Contemporary Physics *
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
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 (IPhT) from 1993-1998 and Head of Institute for the Fundamental Laws of the Universe (IRFU) from 2003 to 2008. He had a position of Scientific Adviser at IRFU from 2008-2025. He also helds the position of Adjunct Professor at Shanghai University and Honorary Pofessor at Suzhou 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, Harvard University and Heidelberg 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. He is member of the French Academy of Sciences and the Academy for Sciences and Literature in Mainz (Germany).
