Sharing symmetries in non-linear systems: Generalized Heisenberg-Weyl algebra on the de Sitter space-time out of the sphere S 3
| Autor: | Julio Becerra Guerrero, Víctor Aldaya, Francisco F. López-Ruiz |
|---|---|
| Přispěvatelé: | Ministerio de Economía y Competitividad (España), Ministerio de Ciencia, Innovación y Universidades (España), European Commission |
| Rok vydání: | 2021 |
| Předmět: |
Non-point symmetries
Pure mathematics Physics and Astronomy (miscellaneous) De Sitter space Non-linear systems Cartan formalism Hamilton–Jacobi 01 natural sciences Hamilton–Jacobi equation S3 sigma model symbols.namesake Symmetry 0103 physical sciences 010306 general physics Mathematics Inverse Noether theorem Weyl algebra 010308 nuclear & particles physics Manifold Symmetry (physics) Homogeneous space symbols Generalized position and momentum in de Sitter space-time Noether's theorem |
| Zdroj: | Digital.CSIC. Repositorio Institucional del CSIC instname |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|