Coherent states for bosons and fermions. Grand partition function. Thermal Green’s functions. Feynman diagrams. Hartree-Fock theory. Gross-Pitaevskij equation. Hubbard-Stratonovich transformations and the BCS theory. Linear response theory and fluctuation-dissipation theorem. Landau Fermi-liquid theory.
John W. Negele, Henri Orland “Quantum Many-Particle Systems”; Alexander L. Fetter, John Dirk Walecka “Quantum Theory of Many-Particle Systems”
Learning Objectives
Knolewdge acquired: Basic formalism for the study of quantum many-particle systems.Competence acquired: Ability to perform calculations for many particle systems by exploiting methods of quantum field theory. Skills acquired (at the end of the course): Capability to investigate equilibrium and out-of-equilibrium properties of nuclear systems, ultracold atomic gases, etc…
Prerequisites
Courses to be used as requirements: (Course recommended) Statistical Mechanics
Teaching Methods
CFU: 6
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 150. Contact hours for Lectures: 48.
Type of Assessment
Oral examination
Course program
Many-body operators in the Fock space. Jellium model for an electron gas. Coherent states for bosons and fermions, Grassmann variables. Grand partition function, thermal Green's functions, perturbative expansions and Feynman diagrams. Dyson’s equation for the self-energy, Hartree-Fock theory. Stationary phase approximation, Gross-Pitaevskij equation and Bose-Einstein condensation of interacting bosons. Hubbard-Stratonovich transformations, auxiliary field, BCS theory for superconductivity. Linear response theory and fluctuation-dissipation theorem. Landau Fermi-liquid theory: equilibrium properties, collective modes, zero-sound.