Course in Quantum Many-Body Theory

This textbook presents various methods to deal with quantum many-body systems, mainly addressing interacting electrons. It focusses on basic tools to tackle quantum effects in macroscopic systems of interacting particles, and on fundamental concepts to interpret the behavior of such systems as revealed by experiments.The textbook starts from simple concepts like second quantization, which allows one to include the indistinguishability and statistics of particles in a rather simple framework, and linear response theory. Then, it gradually moves towards more technical and advanced subjects, including recent developments in the field. The diagrammatic technique is comprehensively discussed. Some of the advanced topics include Landau’s Fermi liquid theory, Luttinger liquids, the Kondo effect, and the Mott transition.The ultimate goal of the book is to gain comprehension of physical quantities that are routinely measured experimentally and fully characterize the system, therefore it is useful for graduate students but also young researchers studying and investigating the theoretical aspects of condensed matter physics.

Michele Fabrizio is full Professor at SISSA – the International School of Advanced Studies in Trieste, Italy. He received the degree in Physics from University “La Sapienza” in Rome, and the PhD in Condensed Matter Theory from SISSA. From 1992 to 1994, he worked as post-doctoral fellow at the Institut Laue-Langevin, Grenoble, France. His research interests mostly concern quantum many-body systems, ranging over the years from one-dimensional conductors to magnetic impurities, molecular superconductors, correlated electron systems and Mott transitions at and out of equilibrium, and unconventional Fermi liquids.