Abstract
We develop the formal basis for the study of independent collections of internally interacting many-particle systems, defined as systems associated with non-overlapping coordinate spaces. We show how ensembles or mixed states of independent many-Fermion systems in their ground states can be described by pure states and give rise to wave functions that are antisymmetric with respect to interchange of particle coordinates (and spin). This is achieved by defining an ensemble Hilbert space whose coordinate representation consists of the tensor sum, rather than product, of the coordinates of the systems in the ensemble. As a demonstration of the power 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, $E_v[N-1]+E_v[N+1]\ge 2E_v[N]$, where $E_v[N]$ denotes the total ground state energy of $N$ electrons under an external potential, $v({\bf r})$.
