Work

Second-order superintegrable systems and Weylian geometry

Year: 2025

Type: article

Abstract: Abundant second-order maximally conformally superintegrable Hamiltonian systems are re-examined, revealing their underlying natural Weyl structure and offering a clearer geometric context for the study of Stäckel transformations (also known as coupling constant metamorphosis). This also allows us to naturally extend the concept of conformal superintegrability from the realm of conformal geometries to that of Weyl structures. It enables us to interpret superintegrable systems of the above type as semi-Weyl structures, a concept related to statistical manifolds and affine hypersurface theory.

Source: Nuclear Physics B

DOI: 10.1016/j.nuclphysb.2025.117095

Author: Andreas Vollmer

Institution: Universität Hamburg

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: Deutsche Forschungsgemeinschaft, Universität Hamburg

Award: Maximal superintegrable Systeme zweiter Ordnung: SemiDegeneriertheit, Separabilität und assoziierte SymmetrieAlgebren.