The behavior of electrons in a metal presents a wide variety of emergent behavior including a number of phase transitions. The mean-field scaling limit acts as a simplified model capturing part of this complexity. In this limit, results going beyond the precision of Hartree-Fock theory have recently been obtained by approximate bosonization methods as a mathematically rigorous version of the random phase approximation. I will review the expansion of the ground state energy and present results extending to the dynamics and momentum distribution of excitations.
