Full Description
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.
Contents
Part one foundations of quantum many body theory.- Quantum mechanics review.- Second quantization for non relativistic identical particles.- Part two a quantum many body model of a solid.- Step one of the solid model bloch electrons.- Step two of the solid model phonons.- Step three of the solid model electron phonon interaction.- Part three developments of quantum many body theory.- Many body greens functions.- Feynmans perturbative theory of the thermal Greens function.- Finite temperature hartree fock method for fermionic systems.- Phonon propagator.- Linear response theory.- Part four further bosonic quantum fields.- Bose einstein condensation of non interacting bosons.- Bogoljubovs theory for interacting boson systems.- Quantization of the electromagnetic field phonons.- Part five toolkit of group theory and symmetries in physics.- Group theory.- Symmetries.- Part six appendices.
