Marcello Porta: On the Correlation Energy of Interacting Fermionic Systems in the Mean-Field Regime

Explore the ground state properties of a homogeneous, interacting Fermi gas in the mean-field regime through this 57-minute lecture from the Hausdorff Junior Trimester Program on Kinetic Theory. Delve into the concept of correlation energy, defined as the difference between many-body and Hartree-Fock ground state energies. Examine recent progress in understanding the precise value of this quantity, including an upper bound that aligns with the Gell-Mann and Brueckner prediction. Investigate the rigorous bosonization technique used to prove this upper bound. Learn about a matching lower bound for small interaction potentials, and gain insights from collaborative research efforts in the field of interacting fermionic systems.