Sharing symmetries in non-linear systems: Generalized Heisenberg-Weyl algebra on the de Sitter space-time out of the sphere S 3

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. © 2021 World Scientific Publishing Company.
We thank the Spanish Ministerio de Ciencia e Innovacin (MICINN) for financial support (FIS2017-84440-C2-2-P) and V. A. acknowledges financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award for the Instituto de Astrofsica de Andaluca (SEV-2017-0709). J. G. acknowledges financial support from the Spanish MICINN (PGC2018-097831B-I00). Discussions with P. Horvathy are also acknowledged.