Stiefel and Grassmann manifolds in quantum chemistry

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• 作者：Eduardo Chiumiento^a ; ^b ; ^{eduardo@mate.unlp.edu.ar} ; Michael Melgaard^c ; ^{mmelgaard@dit.ie}
• 关键词：primary ; 53Z05 ; secondary ; 81V55 ; 22E65 ; 58B20
• 刊名：Journal of Geometry and Physics
• 出版年：2012
• 期刊代码：29_03930440
• 类别：ph
• 出版时间：August, 2012
• 卷：62
• 期：8
• 页码：1866-1881
• 文件大小：304 K

摘要

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.