Description
Oxford From Classical to Quantum Fields 2017 Edition by Laurent Baulieu, John Iliopoulos, Roland Seneor
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 ofquantisation 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 ofthe 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. Table of contents : - 1: Introduction2: Relativistic Invariance3: The Electromagnetic Field4: General relativity: A Field Theory of Gravitation5: The Physical States6: Relativistic Wave Equations7: Towards a Relativistic Quantum Mechanics8: Functional Integrals and Probabilistic Amplitudes9: Functional Integrals and Quantum Mechanics: Formal Developments10: The Euclidean Functional Integrals11: Fermions and Functional Formalism12: Relativistic Quantum Fields13: Applications14: Geometry and Quantum Dynamics15: Broken Symmetries16: Quantum Field Theory at Higher Orders17: A First Glance at Renormalisation and Symmetry18: Renormalisation of Yang-Mills Theory and BRST Symmetry19: Some Consequences of the Renormalisation Group20: Analyticity Properties of Feynman Diagrams21: Infrared Singularities22: Coherent States and Classical Limit of Quantum Electrodynamics23: Quantum Field Theories with a Large Number of Fields24: The Existence of Field Theories beyond the Perturbation Expansion25: Fundamental Interactions26: Beyond the Standard Model27: Supersymmetry, or the Defense of ScalarsAppendix A: Tensor CalculusAppendix B: Differential CalculusAppendix C: Groups and Lie AlgebrasAppendix D: A collection of Useful FormulaeAppendix E: Extract from Maxwell's A Treatise on Electricity and Magnetism