This book presents the lecture notes and exercises corresponding to the course "Quantum Field Theoretical Methods in Condensed Matter" that the authors imparted for several years as part of the masters program on Condensed Matter and Biological Systems at the Autonoma University of Madrid. It provides a step-by-step description of the material which will benefit not only professors wishing to undertake a similar task, but also interested students. Additionally, the book provides a complete set of exercises on the various topics along with hints about how to solve them, a feature frequently absent in textbooks on many-body techniques. As well as addressing the traditional topics in the field (diagrammatic techniques, screening in metals, Fermi liquid theory, electron-phonon interactions, etc.) the text also covers less conventional topics such as the application of non-equilibrium Green function techniques to quantum transport in normal and superconducting nanoscale devices.

Ideally suited master students and professors giving a course on quantum field theory in condensed matter physics Provides a step-by-step exposition of the lectures and exercises, with hints on their solution Include applications to equilibrium and non-equilibrium quantum systems

Autorentext

Alfredo Levy Yeyati obtained his PhD at the University of Buenos Aires in 1989 and became a permanent professor at the Autonoma University of Madrid in 2000. His main research interest is on the theory of quantum transport in meso- and nano-scale systems, with special focus on effects due to superconductivity and electronic correlations. He has been the head of the Theoretical Condensed Matter Physics department at the Autonoma University of Madrid from 2013 to 2022. Jaime Merino obtained his Ph. D at Universidad Autónoma de Madrid (UAM) in1997,followed by postdoctoral research at Brown University, University of New South Wales andthe Max-Planck Institute for Solid State in Stuttgart. He joined the Theoretical CondensedMatter theory Department at UAM as a Ramón y Cajal fellow in 2003 becoming a permanentprofessor in 2011. His research focuses on the physics of strongly correlatedsystemswith particular interest on quantum spin liquids, superconductivity, Mott metal-insulatortransition and out-of-equilibrium many-body phenomena.

Inhalt

Introduction to many-particle physics in Condensed Matter.- Introduction to Green-function methods.- Perturbation theory at zero temperature.- Finite temperature Green function formalism.- Linear response and collective modes.- Generalized Green function propagator.- Introduction to non-equilibrium: the Keldysh contour.- Perturbative expansion in the non-equilibrium formalism.- Applications: electron transport at the nanoscale.- Introduction to path integral methods.- Application of path integral methods: the renormalization group approach.- Hints for solving exercises