Document Type

Article

Rights

This item is available under a Creative Commons License for non-commercial use only

Disciplines

Pure mathematics, Applied mathematics, Atomic, Molecular and Chemical Physics

Publication Details

To appear in Journal of Geometry and Physics (2012).

Online: http://www.sciencedirect.com/science/article/pii/S0393044012000927

Abstract

We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slatertype variational spaces in many-particle Hartree-Fock theory and beyond. In particular, we prove thatthey are analytic homogeneous spaces and submanifolds of the space of bounded operators on the single-particle Hilbert space. As a by-product we obtain that they are complete Finsler manifolds. These geometric properties underpin state-of-the-art results on existence of solutions to Hartree-Fock type equations.