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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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Official URL: http://dx.doi.org/10.1016/j.geomphys.2012.04.005
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 |
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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 |