Remarks on Density-Matrix-Functional Theory

Density functional theory is moving towards a more complicated version called Density-Matrix-Functional Theory, of which Hartree-Fock theory is an old example. A modification of Hartree-Fock theory due to Mueller is now being used by several researchers. The mathematical foundations (existence and uniqueness of energy minimizers, etc.) are, however, more complicated than for Hartree-Fock theory; in work with R. Frank, R. Seiringer and H. Siedentop we have been able to address the most important questions, but some interesting ones still remain.