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 fundamentalinteractions. 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 aunified 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 superfluidtransitions; 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 symmetriesare 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. Exercises that were originally included in previous editions will be supplied online atwww-spht.ceafr/articles/T02/001.

This work provides a systematic introduction to quantum field theory and renormalization group, as applied to particle physics and continuous macroscopic phase transitions.

An introduction to quantum field theory and renormalization groups. This text shows that these frameworks are essential for the understanding of phenomena belonging to many different areas of physics.

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 well-received work is now available in a new edition. It is an advanced text on quantum field theory--which is not only the accepted framework for describing all fundamental interactions except gravity, but also for understanding second-order phase transitions in statistical mechanics. The book approaches this subject in terms of path and functional integrals. A Euclidean metric has been adopted and the language of partition and correlation functions is used. Renormalization and the renormalization group are also discussed. Full mathematical details are provided. The text is intended for theoretical particle physicists and statistical physicists at the graduate level and above.

Over the last twenty years quantum field theory has become not only the framework for the discussion of all fundamental interactions except gravity, but also for the understanding of second-order phase transitions in statistical mechanics.This advanced text is based on graduate courses and summer schools given by the author over a number of years. It approaches the subject in terms of path and functional intergrals, adopting a Euclidean metric and using the language of partition and correlation functions. Renormalization and therenormalization group are examined, as are critical phenomena and the role of instantons.Changes for this edition1. Extensive revision to eliminate a few bugs that had survived the second edition and (mainly) to improve the pedagogical presentation, as a result of experience gathered by lecturing.2. Additional new topics; holomorphic or coherent state path integral; functional integral and representation of the field theory S-matrix in the holomorphic formalis; non-relativistic limit of massive quantization and brief discussion of non-renormalization of quantum gravity based on Einsteinaction.3. Finally 65 pages of solutions or hints of solutions to the exercises at the ends of chapters.

Over the last twenty years quantum field theory has become not only the framework for the discussion of all fundamental interactions (except gravitation) but also for the understanding of second-order phase transitions in statistical mechanics. This advanced volume is based on graduate courses and summer schools given over a number of years by the author. It approaches the subject in terms of path and functional integrals. A Euclidean metric has been adopted and the language of partition and correlation functions is used. Renormalization and the renormalization group are discussed. A major part of the book is devoted to critical phenomena before concluding with a discussion of the role of instantons in quantum field theory.