Quantum groups, non-commutative Lorentzian spacetimes and curved momentum spaces
| Autor: | Gutiérrez-Sagredo, I., Ballesteros Castañeda, Ángel, Gubitosi, G., Herranz, F.J. |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | UVaDOC. Repositorio Documental de la Universidad de Valladolid Consejo Superior de Investigaciones Científicas (CSIC) |
| DOI: | 10.48550/arxiv.1907.07979 |
| Popis: | The essential features of a quantum group deformation of classical symmetries of General Relativity in the case with non-vanishing cosmological constant $\Lambda$ are presented. We fully describe (anti-)de Sitter non-commutative spacetimes and curved momentum spaces in (1+1) and (2+1) dimensions arising from the $\kappa$-deformed quantum group symmetries. These non-commutative spacetimes are introduced semiclassically by means of a canonical Poisson structure, the Sklyanin bracket, depending on the classical $r$-matrix defining the $\kappa$-deformation, while curved momentum spaces are defined as orbits generated by the $\kappa$-dual of the Hopf algebra of quantum symmetries. Throughout this construction we use kinematical coordinates, in terms of which the physical interpretation becomes more transparent, and the cosmological constant $\Lambda$ is included as an explicit parameter whose $\Lambda \rightarrow 0$ limit provides the Minkowskian case. The generalization of these results to the physically relevant (3+1)-dimensional deformation is also commented. Comment: Based on the contribution presented at the "First Hermann Minkowski Meeting on the Foundations of Spacetime Physics" held in Albena, Bulgaria, May 15-18, 2017 |
| Databáze: | OpenAIRE |
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