Understanding Quantum Many-Body Theory

This textbook offers a rigorous, self-contained introduction to quantum many-body theory, developed from lecture notes at the University of Naples Federico II. Worked examples, solved exercises, and detailed derivations are woven throughout, guiding readers in the formulation and analysis of advanced theoretical and numerical models. Where possible, exact solutions are included to clarify the structure of many-body techniques and deepen understanding of their applications. The result is both a reliable theoretical reference and a practical resource for strengthening conceptual and computational skills.

The textbook is aimed primarily at advanced undergraduates and first-year master s students in physics who are beginning the study of interacting quantum systems, at both zero and finite temperature. A concise review of quantum mechanics covering key concepts and formalism opens the book. Core topics include second quantization, phonons, electron phonon interaction, the Hartree Fock method for fermionic systems, Bogoliubov theory for bosonic systems, many-body Green s functions, Feynman diagrams, linear-response theory, Bose Einstein condensation, and quantization of the electromagnetic field. The volume concludes with two concise toolkit chapters on elements of group theory for physicists and symmetries, serving as supplementary algebraic background.