Lobachevsky geometry in TTW and PW systems
Tigran Hakobyan, Armen Nersessian, Hovhannes Shmavonyan
TL;DR
This paper reviews the properties and hidden symmetries of TTW and PW systems, linking them to Calogero models, and introduces a complex coordinate approach to describe their symmetries using action-angle variables.
Contribution
It presents a novel complex coordinate method to analyze hidden and dynamical symmetries in TTW and PW systems, connecting them with Calogero models.
Findings
Identified hidden symmetries in TTW and PW systems.
Established a complex coordinate framework for symmetry analysis.
Linked these systems' symmetries with N-dimensional Calogero models.
Abstract
We review the classical properties of Tremblay-Turbiner-Winternitz and Post-Wintenitz systems and their relation with N-dimensional rational Calogero model with oscillator and Coulomb potentials, paying special attention to their hidden symmetries. Then we show that combining the radial coordinate and momentum in a single complex coordinate in proper way, we get an elegant description for the hidden and dynamical symmetries in these systems related with action-angle variables.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.