From Classical to Quantum Fields

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, theTheory 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.

• 1: Introduction 2: Relativistic Invariance 3: The Electromagnetic Field 4: General relativity: A Field Theory of Gravitation 5: The Physical States 6: Relativistic Wave Equations 7: Towards a Relativistic Quantum Mechanics 8: Functional Integrals and Probabilistic Amplitudes 9: Functional Integrals and Quantum Mechanics: Formal Developments 10: The Euclidean Functional Integrals 11: Fermions and Functional Formalism 12: Relativistic Quantum Fields 13: Applications 14: Geometry and Quantum Dynamics 15: Broken Symmetries 16: Quantum Field Theory at Higher Orders 17: A First Glance at Renormalisation and Symmetry 18: Renormalisation of Yang-Mills Theory and BRST Symmetry 19: Some Consequences of the Renormalisation Group 20: Analyticity Properties of Feynman Diagrams 21: Infrared Singularities 22: Coherent States and Classical Limit of Quantum Electrodynamics 23: Quantum Field Theories with a Large Number of Fields 24: The Existence of Field Theories beyond the Perturbation Expansion 25: Fundamental Interactions 26: Beyond the Standard Model 27: Supersymmetry, or the Defense of Scalars Appendix A: Tensor Calculus Appendix B: Differential Calculus Appendix C: Groups and Lie Algebras Appendix D: A collection of Useful Formulae Appendix E: Extract from Maxwell's A Treatise on Electricity and Magnetism

From Classical to Quantum Fields makes for a fine companion for students and an excellent general reference for researchers in theoretical physics.