These are lecture notes based on three lectures given by Antonello Scardicchio at the December 2016 Topical School on Many-Body-Localization organized by the Statistical Physics Group of the Institute Jean Lamour in Nancy. They were compiled and put in a coherent logical form by Thimothée Thiery.
In these notes, we present a rigorous and self-contained introduction to the fundamental concepts and methods of quantum many-body theory. The text is designed to provide a solid theoretical foundation for the study of interacting quantum systems, combining clarity with mathematical precision. Core topics are developed systematically, with detailed derivations and comprehensive proofs that aim to make the material accessible to graduate students and beginning PhD students. Special attention is given to formal consistency and pedagogical structure, so as to guide the reader through both the conceptual and technical aspects of the subject. This work is intended as a reliable starting point for further exploration and research in modern quantum many-body physics.
From July 21 to August 9, 1958, a summer course on Mathematical Problems of Quantum Theory of Particles and Fields was held in Varenna, Italy. The lectures took place in the Villa Monastero, on the shores of beautiful Lake Como; the place is well known to the readers of Physics Today since in other issues (Dec. 1957, Jan. 1958) there have been reports about conferences held there, and about other courses of the International School of Physics. The school is organized by the Italian Physical Society and is sponsored by the Italian National Science Council, by the Italian Government, by some Italian universities, by various local representatives, and occasionally by other institutions. Each summer it gives a number of courses (recently three or four), on special topics in physics. These courses are neither meetings of experts, nor quick courses at the graduate-school level. The goal is to put the persons with most experience in a field in touch with the younger or less experienced, in order to give the latter an up-to-date picture of recent research and open problems. The courses are organized quite independently and vary in length from a few days to three weeks in the present case.