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 masters students in physics who are beginning the study of interacting quantum systems, at both zero and finite temperature. A concise review of quantum mechanicscovering key concepts and formalismopens the book. Core topics include second quantization, phonons, electronphonon interaction, the HartreeFock method for fermionic systems, Bogoliubov theory for bosonic systems, many-body Greens functions, Feynman diagrams, linear-response theory, BoseEinstein 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.
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.
Fabrizio Tafuri earned his Masters degree in Physics from the University of Naples "Federico II" in 2021 with a thesis on statistical mechanics applied to biological systems. He has authored six publications in classical and quantum statistical mechanics. Currently on his second research fellowship, he focuses on many-body quantum field theory. His broader research interests include equilibrium and non-equilibrium statistical physics, studied through analytical and numerical methods.
Carmine Antonio Perroni received his Ph.D. in Physics from the University of Naples "Federico II" in 2002. He is Associate Professor of Theoretical Physics of Matter in the Department of Physics "E. Pancini" at the same university. Since 2007, he has taught courses including General Physics for students in Pharmacy and Information Engineering, Quantum Many-Body Theory for physics masters students, and Elements of Physics of Matter for physics undergraduates. His research focuses on the electronic, magnetic, and superconducting properties of strongly correlated bulk materials, heterostructures, and nanostructures. More recently, he has investigated quantum systems coupled to external baths and leads, employing both analytical methods and equilibrium and non-equilibrium Greens functions. He is the author of about 100 papers published in peer-reviewed journals.
Giulio De Filippis received his degree in Physics, cum laude, from the University of Naples "Federico II" in 1985, and a Ph.D. in General and Applied Physics from the University of Salerno in 1998. Since 2015, he has been Associate Professor of Theoretical Physics of Matter at the University of Naples "Federico II." He has authored over 100 publications in leading international journals. Since 2002, he has taught courses such as General Physics for students in Chemistry and Pharmaceutical Technologies and Quantum Many-Body Theory for physics masters students. His research interests include high-temperature superconductivity in cuprates, ultrafast quasiparticle dynamics in strongly correlated electron systems, charge transport in organic semiconductors, many-body open quantum systems, quantum information theory, topological insulators, and quantum thermodynamics.
