On the quantum field theory of the inhomogeneous electron gas

The equilibrium properties of an inhomogeneous gas of interacting fermions are derived using methods of finite temperature quantum field theory. A Landau-type quasiparticle spectrum yielding the exact ground state energy or, at finite temperatures, the exact thermodynamic potential is constructed from the g-Hartree equations. The heat kernel expansion of Schrodinger operators is then used to express the Hohenberg-Kohn density functional as a series in the quasiparticle density which is asymptotic in the Thomas-Fermi limit. This series is systematically derived from the microscopic action and incorporates boundary effects in an unambiguous manner. The methods developed apply to a large class of field-theoretical models encompassing theories with Yukawa interactions.