Local approximation for the hartree-fock exchange potential: A deformation approach

We present a method for deriving local approximations of the exchange-term in the Hartree-Fock equation for a system of fermions interacting with a Coulomb-force. Within our model, we give a justification of the Slater-approximation where the exchange-term is replaced by the third root of the local density. Our approach is based on deformations, i.e. local scaling transformations of a constant density, combined with the "high density limit" of infinite number of particles.