Homogeneous spaces in Hartree-Fock-Bogoliubov theory

Autor:	Alvarado, Claudia D., Chiumiento, Eduardo
Rok vydání:	2024
Předmět:	Mathematics - Functional Analysis Mathematical Physics Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	We study the action of Bogoliubov transformations on admissible generalized one-particle density matrices arising in Hartree-Fock-Bogoliubov theory. We show that the orbits of this action are reductive homogeneous spaces, and we give several equivalences that characterize when they are embedded submanifolds of natural ambient spaces. We use Lie theoretic arguments to prove that these orbits admit an invariant symplectic form. If, in addition, the operators in the orbits have finite spectrum, or infinite spectrum and trivial kernel, then we obtain that the orbits are actually K\"ahler homogeneous spaces. Comment: 43 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.15606 Zobrazit plný text záznamu View this record from Arxiv