Quantum Theory of Many-Body Systems Techniques and Applications - Zagoskin, Alexandre; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2014)
This text presents a self-contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, uses the mathematical formalism of quasiparticles and Green’s functions. In particular, it covers all the important diagram techniques for normal and superconducting systems, including the zero-temperature perturbation theory and the Matsubara, Keldysh and Nambu-Gor'kov formalism, as well as an introduction to Feynman path integrals. This new edition contains an introduction to the methods of theory of one-dimensional systems (bosonization and conformal field theory) and their applications to many-body problems.   Intended for graduate students in physics and related fields, the aim is not to be exhaustive, but to present enough detail to enable the student to follow the current research literature, or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum coherence is maintained throughout their volume, and which therefore provides an ideal testing ground for many-body theories.
Basic Concepts -- Green’s Functions at Zero Temperature -- More Green’s Functions, Equilibrium and Otherwise and Their Applications -- Methods of Many-Body Theory in Superconductivity. Many-Body Theory in One Dimension -- A: Friedel Oscillations -- B: Landauer Formalism for Hybrid Normal-Superconducting Structures.
Keywords: Superconductivity; Superconductors; Mathematical physics; Quantum physics; System theory; Condensed matter; Quantum computers; Spintronics; Strongly Correlated Systems, Superconductivity; Mathematical Applications in the Physical Sciences; Quantum Physics; Complex Systems; Condensed Matter Physics; Quantum Information Technology, Spintronics