Antisymmetric wave functions for mixed fermion states and energy convexity

We show how ensembles or mixed states can be described in terms of pure states that for Fermions lead to wave functions that are antisymmetric with respect to interchange of particle coordinates (and spin). The pure states are constructed in an augmented Hilbert space spanned by products of ensemble states projected onto mutually nonoverlapping coordinates that prevents the appearance of interference terms under antisymmetrization. As a demonstration of this new formalism, and under the assumptions of a positive interparticle interaction and a corresponding energy that is extensive in the number of particle pairs (pair extensive), we prove the convexity relation, E-v [N - 1] + E-v[N + 1] >= 2E(v)[N], where E-v[N] denotes the total ground-state energy of N Fermions (electrons) under an external potential v(r).