Many-Body Problems and Quantum Field Theory

Abstract

Summary: The book gives an introduction to the concepts and methods of many-body problems and quantum fields for graduate students and researchers. The formalism is developed in close conjunction with the description of a number of physical systems: cohesion and dielectric properties of the electron gas, superconductivity, superfluidity, nuclear matter and nucleon pairing, matter and radiation, interaction of fields by particle exchange and mass generation. Emphasis is put on analogies between the various systems rather than on advanced or specialized aspects, with the purpose of illustrating common ideas in different domains of physics. The exposition is self-contained and displays in a coherent way all details of derivations starting from a basic knowledge of quantum mechanics and classical electromagnetism. 1. Classical Fields and Their Associated Particles -- 2. Fermions and Bosons -- 3. Systems with Variable Particle Number -- 4. Electron Gas -- 5. Fermion Pairing and Superconductivity -- 6. Nucleon Pairing and the Structure of the Nucleus -- 7. The Superfluidity of Liquid Helium -- 8. Quantum Fields -- 9. Perturbative Methods in Field Theory -- 10. Perturbative Methods in Many-Body Problems.