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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.
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