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This book provides a pedagogical introduction to the concepts and methods of quantum field theory necessary for the study of condensed matter and ultracold atomic gases. After a thorough discussion of the basic methods of field theory and many-body physics (functional integrals, perturbation theory, Feynman diagrams, correlation functions and linear response theory, symmetries and their consequences, etc.), the book covers a wide range of topics, from electron gas and Fermi-liquid theory to superfluidity and superconductivity, magnetic instabilities in electron systems, and dynamical mean-field theory of Mott transition. The focus is on the study of model Hamiltonians, where the microscopic physics and characteristic energy scales are encoded into a few effective parameters, rather than first-principle methods which start from a realistic Hamiltonian at the microscopic level and then make material-specific predictions. The reader is expected to be familiar with elementary quantum mechanics and statistical physics, and some acquaintance with condensed-matter physics and ultracold gases may also be useful. No prior knowledge of field theory or many-body problem is required.
Preface
Acknowledgments
Acronyms
List of Symbols and Notations
Functional Integrals, Symmetries, and Correlation Functions
Functional Integrals
Symmetries
Correlation and Response Functions
Quantum Many-Body Systems (I)
Fermi-Liquid Theory
The Electron Gas
Magnetism in Lattice Fermion Systems
Superfluidity and Superconductivity
Quantum Magnetism
Baym–Kadanoff Formalism
Index