Sharing symmetries in non-linear systems: Generalized Heisenberg-Weyl algebra on the de Sitter space-time out of the sphere S3

DOI: 
10.1142/S0219887821500742
Publication date: 
01/01/1970
Main author: 
Aldaya, Victor
IAA authors: 
Aldaya, Victor
Authors: 
Aldaya, Victor;Guerrero, Julio;López-Ruiz, Francisco F.
Journal: 
International Journal of Geometric Methods in Modern Physics
Publication type: 
Article
Volume: 
18
Pages: 
2150074-1354
Abstract: 
In this paper, we exploit the formal equivalence of the Solution Manifold of two distinct physical systems to create enough symmetries so as to characterize them by Noether Invariants, thus favoring their future quantization. In so doing, we somehow generalize the Arnold Transformation for non-necessarily linear systems. Very particularly, this algorithm applies to the case of the motion on the de Sitter space-time providing a finite-dimensional algebra generalizing the Heisenberg-Weyl algebra globally. In this case, the basic (contact) symmetry is imported from the motion of a (non-relativistic) particle on the sphere S3.
Database: 
ADS
URL: 
https://ui.adsabs.harvard.edu/#abs/2021IJGMM..1850074A/abstract
ADS Bibcode: 
2021IJGMM..1850074A
Keywords: 
Symmetry;non-linear systems;non-point symmetries;Cartan formalism;Hamilton–Jacobi;inverse Noether theorem;S3 sigma model;generalized position and momentum in de Sitter space-time