Introduction to Classical and Quantum Field Theory

1. Introduction -- 2. Basics of Classical Field Theory -- 3. Quantization of Classical Field Theories (I) -- 4. Quantization of Classical Field Theories (II) -- 5. Perturbation Theory, Variational Approach and Correlation Functions -- 6. Introduction to Berry Phase and Gauge Theory -- 7. Introduction to Effective Field Theory, Phases, and Phase Transitions -- 8. Solitons, Instantons, and Topology in QFT -- 9. Simple Boson Liquids: Introduction to Superfluidity -- 10. Simple Fermion Liquids: Introduction to Fermi Liquid Theory -- 11. Superconductivity: BCS Theory and Beyond -- 12. Introduction to Lattice Gauge Theories -- Appendix. One-Particle Green's Function in Second-Order Perturbation Theory. This is the first introductory textbook on quantum field theory to be written from the point of view of condensed matter physics. As such, it presents the basic concepts and techniques of statistical field theory, clearly explaining how and why they are integrated into modern (and classical) field theory, and includes the latest developments. Written by an expert in the field, with a broad experience in teaching and training, it manages to present such substantial topics as phases and phase transitions or solitons and instantons in an accessible and concise way. Divided into two parts, the first covers fundamental physics and the mathematics background needed by students in order to enter the field, while the second part discusses applications of quantum field theory to a few basic problems. The emphasis here lies on how modern concepts of quantum field theory are embedded in these approaches, and also on the limitations of standard quantum field theory techniques in facing 'real' physics problems. Throughout, there are numerous end-of-chapter problems, and a free solutions manual is available for lecturers.