This book compiles the notes from a course in many-body physics, presented for nearly 20 years to graduate students at the University of Salento held by the author. It is intended for students already familiar with basic non-relativistic quantum mechanics. Building on this foundation, the book explores the challenges that arise when traditional quantum mechanics approaches are applied to systems composed of many interacting particles, such as nuclei, electron gas, multi-electron atoms, complex molecules, and quantum liquids.

The first part of the book introduces the quantum many-body problem and provides essential information. The second part describes the Monte Carlo approach which solves the problem without approximations and its technical limitations are emphasized. In the third part, the approaches inspired by quantum field theory are presented. The theoretical entities used here are creation and destruction operators, Green's functions, and propagators. The theories are focused on the modifications of the interaction between the particles when they interact in a medium. In the fourth part, various theories inspired by statistical mechanics are discussed, with an emphasis on the correlations between particles in the system. The fifth part covers phenomenological theories, where the interaction between particles is defined within the framework of the theory itself to describe certain properties of the many-body system.

The aim of the book is to provide graduate students with a comprehensive overview of the fundamental ideas related to the theories used to address the quantum many-body problem. Since the text is intended for students rather than experts in the field, detailed calculations are presented, with a focus on the basic concepts underlying the various theories rather than on recent numerical advancements, which are continually evolving.

Explores diverse approaches to the Quantum-Many Body problem offering comprehensive insights to students and researchers Details calculations explicitly, ensuring clarity and precision for readers Requires only basic non-relativistic quantum mechanics knowledge

Autorentext

Giampaolo Co' graduated from the University of Bologna and obtained his Ph.D. at the University of Bonn. He was a Ph.D. student and Post-Doc at the Kernforschungszentrum in Juelich (Germany), at the University of Champaign-Urbana (Illinois), and research associate at the Lecce division of the National Institute of Nuclear Physics. Since 1992, he has been associate professor of Nuclear Physics at the University of Salento, where he teaches courses in thermodynamics, nuclear and subnuclear physics, quantum mechanics, and quantum theory of many-body systems. His research has always been focused on applying quantum many-body techniques to the study of strongly interacting nuclear systems. In particular, he has been interested in nuclear systems response to electroweak probes, photons, electrons, and neutrinos. He is the author of about 80 research articles and other 50 scientific publications. He is a scientific editor of Ithaca, an Italian popular science journal.

Inhalt

Introducing the Many-body Problem.- Basic Information.- Mean-field.- Solutions Without Approximations.- Theories Inspired to Quantum Field Theories.- Occupation Number.- Perturbation Theory of Many-body Systems.- Goldstone Theorem.- Brueckner Theory.- Green's Function.- Perturbative Description of the Green's.- Theories Inspired to Statistical Mechanics.- Correlated Basis Function Theory.- Unitary Correlation Operator Method.- The Coupled Cluster Method.- Phenomenological Theories.- Effective Theories.- Mean-field Applications of the Variational Principle.- Excited States.- The Fermi Liquid Theory.