PERIOD: NOVEMBER - JANUARY This course presents the quantum-field theory approach to many-body systems. The main topics discussed are: the lagrangian/hamiltonian formulation of classical mechanics and the Hamilton approach to classical field theory, the quantization of nonrelativistic Schroedinger equation and the definition of creation, destruction, and number operators, the properties of bosonic/fermionic fields (and, in particular, the notion of Fermi-Dirac and Bose-Einstein statistics, the Pauli principle and the spin-statistics theorem), and the Bose-Einstein gas of interacting particles within the Bogoliubov scheme. The field-theory approach is then applied to derive the Bose-Hubbard model currently employed to describe condensed bosons trapped in optical lattices. Finally, the statistical-mechanics approach to the ideal Bose-Einstein and Fermi-Dirac gases is discussed.

Course contents: The Lagrange and Hamilton formulation of classical dynamics; Hamilton approaches to Classical field theory. Nonrelativistic quantum field theory of many-body systems: Quantization of Schroedinger equation; the N representation, creation, destruction and number operators. Properties of bosonic and fermionic fields; Bose-Einstein and Fermi-Dirac statistics; Pauli principle and spin statistics theorem; From many-body systems to quantum field theory; nearly-ideal, degenerate BE gases: Bogoliubov approach; superfluidity. The Bose-Hubbard model for condensed bosons trapped in optical lattices. Statistical mechanics of ideal Bose-Einstein and Fermi-Dirac gases.

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Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.