RT Journal Article
T1 Classical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry
A1 Reyes Nozaleda, Daniel
A1 Tempesta, Piergiulio
A1 Tondo, Giorgio
AB We show that the theory of classical Hamiltonian systems admitting separating variables can be formulated in the context of (omega, H ) structures. They are symplectic manifolds en-dowed with a compatible Haantjes algebra H , namely an algebra of (1,1)tensor fields with vanishing Haantjes torsion. A special class of coordinates, called Darboux-Haantjes coor-dinates, will be constructed from the Haantjes algebras associated with a separable sys-tem. These coordinates enable the additive separation of variables of the corresponding Hamilton-Jacobi equation. We shall prove that a multiseparable system admits as many omega H structures as sepa-ration coordinate systems. In particular, we will show that a large class of multiseparable, superintegrable systems, including the Smorodinsky-Winternitz systems and some physi-cally relevant systems with three degrees of freedom, possesses multiple Haantjes struc-tures. (C) 2021 Published by Elsevier B.V.
PB Elsevier
SN 1007-5704
YR 2022
FD 2022-01
LK https://hdl.handle.net/20.500.14352/72439
UL https://hdl.handle.net/20.500.14352/72439
LA eng
NO © 2022 ElsevierThe research of D. R. N. has been supported by the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000904-S), Ministerio de Ciencia, Innovacion y Universidades, Spain. The research of P. T. has been supported by the research project PGC2018-094898-B-I00, Ministerio de Ciencia, Innovacion y Universidades, Spain, and by the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000904-S), Ministerio de Ciencia, Innovacion y Universidades, Spain. The research of G. T. has been supported by the research project FRA2020-2021, Universitadegli Studi di Trieste, Italy. P. T. is member of Gruppo Nazionale di Fisica Matematica (GNFM) of INDAM.
NO Ministerio de Ciencia e Innovación (MICINN)
NO Centros de Excelencia Severo Ochoa (MICINN)
NO Universitá degli Studi di Trieste
DS Docta Complutense
RD 17 may 2024