Stiefel and Grassmann manifolds in quantum chemistry

Chiumiento, Eduardo and Melgaard, Michael (2012) Stiefel and Grassmann manifolds in quantum chemistry. Journal of Geometry and Physics, 62 (8). pp. 1866-1881. ISSN 0393-0440

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Abstract

We establish geometric properties of Stiefel and Grassmann manifolds which arise in relation to Slater type variational spaces in many-particle Hartree–Fock theory and beyond. In particular, we prove that they 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 the existence of solutions to Hartree–Fock type equations.

Item Type: Article
Keywords: Variational spaces in Hartree–Fock theory; Banach–Lie group; Homogeneous space; Finsler manifold
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Richard Chambers
Date Deposited: 20 May 2013 14:16
Last Modified: 20 May 2013 14:16
URI: http://sro.sussex.ac.uk/id/eprint/44771
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