(Anti)de Sitter/Poincare symmetries and representations from Poincare/Galilei through a classical deformation approach
| dc.creator | Herranz, Francisco J. | |
| dc.creator | Santander, Mariano | |
| dc.date | 2006-12-19 | |
| dc.date | 2007-12-12 | |
| dc.date.accessioned | 2026-07-07T11:23:46Z | |
| dc.date.available | 2026-07-07T11:23:46Z | |
| dc.description | A classical deformation procedure, based on universal enveloping algebras, Casimirs and curvatures of symmetrical homogeneous spaces, is applied to several cases of physical relevance. Starting from the (3+1)D Galilei algebra, we describe at the level of representations the process leading to its two physically meaningful deformed neighbours. The Poincare algebra is obtained by introducing a negative curvature in the flat Galilean phase space (or space of worldlines), while keeping a flat spacetime. To be precise, starting from a representation of the Galilei algebra with both Casimirs different from zero, we obtain a representation of the Poincare algebra with both Casimirs necessarily equal to zero. The Poincare angular momentum, Pauli-Lubanski components, position and velocity operators, etc. are expressed in terms of "Galilean" operators through some expressions deforming the proper Galilean ones. Similarly, the Newton-Hooke algebras appear by endowing spacetime with a non-zero curvature, while keeping a flat phase space. The same approach, starting from the (3+1)D Poincare algebra provides representations of the (anti)de Sitter as Poincare deformations. | |
| dc.description | 19 pages, LaTeX.7. Comments and references added | |
| dc.identifier | https://arxiv.org/abs/math-ph/0612059 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0612059 | |
| dc.identifier | J.Phys.A41:015204,2008 | |
| dc.identifier | doi:10.1088/1751-8113/41/1/015204 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/195004 | |
| dc.subject | Mathematical Physics | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | (Anti)de Sitter/Poincare symmetries and representations from Poincare/Galilei through a classical deformation approach | |
| dc.type | text |