Random phase approximation for the mean-field electron gas

Random phase approximation (RPA) was proposed by Bohm and Pines to describe the correction to the Hartree-Fock theory. The heuristic derivation of the RPA has included notable work by theoretical physicists since the 1950s but the mathematical understanding remains very challenging. In this talk, I will discuss a rigorous bosonization method where suitable pairs of fermions are described by a quasi-bosonic Bogoliubov Hamiltonian, leading to a precise leading order formula of the correlation energy of electrons in the mean-field regime. This is joint work with M. R. Christiansen and C. Hainzl.