Introduction to Green's Function Methods in Many-Body Physics: With Applications to Quantum Transport

This book provides a comprehensive introduction to equilibrium and non-equilibrium Green's function methods in many-body physics.It begins with a derivation of second quantisation for relativistic systems based on the many-body relativistic Dirac equation and its non-relativistic limit.The properties of equilibrium Green's functions are then described, with discussion of the two-time and Matsubara Green's function methods.The coverage of non-equilibrium Green's function methods includes the diagrammatic techniques applicable to electrons and phonons using both the perturbation and variational approaches.Specific applications to steady-state and time-dependent quantum transport are presented in the final chapters.The book's accessible explanations, detailed derivations, and systematic treatment of the underlying theory make it a valuable resource for graduate students and early-career researchers.More than 200 problems have been included to support learning, with selected solutions avai