From Classical to Quantum Fields

Quantum Field Theory has become the universal language of most modern theoretical physics. This introductory textbook shows how this beautiful theory offers the correct mathematical framework to describe and understand the fundamental interactions of elementary particles. The book begins with a brief reminder of basic classical field theories, electrodynamics and general relativity, as well as their symmetry properties, and proceeds with the principles of quantisation following Feynman's path integral approach. Special care is used at every step to illustrate the correct mathematical formulation of the underlying assumptions. Gauge theories and the problems encountered in their quantisation are discussed in detail. The last chapters contain a full description of the Standard Model of particle physics and the attempts to go beyond it, such as grand unified theories and supersymmetry. Written for advanced undergraduate and beginning graduate students in physics and mathematics, the book could also serve as a reference for active researchers in the field.

Laurent Baulieu is currently CNRS Research Director at the University of Paris, where he has long been the head of the Theoretical Physics Department. His main field of research is Quantum Field Theory, the Theory of Elementary Particles and Symmetries. He has been an organizer of many summer schools and workshops on various aspects of Quantum Field Theory, especially in les Houches and in the Cargèse Institute in Corsica. John Iliopoulos is Director of Research Emeritus at the Ecole Normale Supérieure in Paris, where for many years he was the head of the Theoretical Physics Department. His research was centred around theoretical particle physics. In 1970, in collaboration with Sheldon Glashow and Luciano Maiani, he predicted the existence of the charm quark and proposed the GIM mechanism, an important step in the construction of the Standard Model. He has also contributed to the development of supersymmetry (with Bruno Zumino and Pierre Fayet). He has received many awards, such as the Ricard Prize of the French Physical Society, the Sakurai Prize of the American Physical Society, the High Energy Physics Prize of the European Physical Society and the Dirac Medal. Roland Sénéor is Director of Research Emeritus at the French CNRS. He spent most of his career at the Ecole Polytechnique, where he established and directed the Graduate School and was the Head of the Department for International Scientific Relations. His research centered on the mathematical foundations of QFT: the axiomatic formulation, the constructive approach, the summability of the perturbation expansion and the study of dynamic stochastic models. He has received various awards, including the Langevin Prize of the French Physical Society.