Quantum Field Theory and Critical Phenomena: Fifth Edition

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.

Jean Zinn-Justin, Member of the French Academy of Sciences and the Academy for Sciences and Literature in Mainz, Germany, IRFU/CEA, Paris-Saclay University

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).