The κ-Newtonian and κ-Carrollian algebras and their noncommutative spacetimes
We derive the non-relativistic c→∞ and ultra-relativistic c→0 limits of the κ-deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the κ-(A)dS quantum algebra, and qu...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2020-06-01
|
| Series: | Physics Letters B |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269320302653 |
| _version_ | 1819058506070753280 |
|---|---|
| author | Angel Ballesteros Giulia Gubitosi Ivan Gutierrez-Sagredo Francisco J. Herranz |
| author_facet | Angel Ballesteros Giulia Gubitosi Ivan Gutierrez-Sagredo Francisco J. Herranz |
| author_sort | Angel Ballesteros |
| collection | DOAJ |
| description | We derive the non-relativistic c→∞ and ultra-relativistic c→0 limits of the κ-deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the κ-(A)dS quantum algebra, and quantize the resulting contracted Poisson–Hopf algebras, thus giving rise to the κ-deformation of the Newtonian (Newton–Hooke and Galilei) and Carrollian (Para-Poincaré, Para-Euclidean and Carroll) quantum symmetries, including their deformed quadratic Casimir operators. The corresponding κ-Newtonian and κ-Carrollian noncommutative spacetimes are also obtained as the non-relativistic and ultra-relativistic limits of the κ-(A)dS noncommutative spacetime. These constructions allow us to analyze the non-trivial interplay between the quantum deformation parameter κ, the curvature parameter η and the speed of light parameter c. |
| first_indexed | 2024-12-21T13:56:17Z |
| format | Article |
| id | doaj.art-a168507a34874f50af30998902cef755 |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-12-21T13:56:17Z |
| publishDate | 2020-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-a168507a34874f50af30998902cef7552022-12-21T19:01:32ZengElsevierPhysics Letters B0370-26932020-06-01805The κ-Newtonian and κ-Carrollian algebras and their noncommutative spacetimesAngel Ballesteros0Giulia Gubitosi1Ivan Gutierrez-Sagredo2Francisco J. Herranz3Departamento de Física, Universidad de Burgos, 09001 Burgos, Spain; Corresponding author.Departamento de Física, Universidad de Burgos, 09001 Burgos, SpainDepartamento de Física, Universidad de Burgos, 09001 Burgos, Spain; Departamento de Matemáticas y Computación, Universidad de Burgos, 09001 Burgos, SpainDepartamento de Física, Universidad de Burgos, 09001 Burgos, SpainWe derive the non-relativistic c→∞ and ultra-relativistic c→0 limits of the κ-deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the κ-(A)dS quantum algebra, and quantize the resulting contracted Poisson–Hopf algebras, thus giving rise to the κ-deformation of the Newtonian (Newton–Hooke and Galilei) and Carrollian (Para-Poincaré, Para-Euclidean and Carroll) quantum symmetries, including their deformed quadratic Casimir operators. The corresponding κ-Newtonian and κ-Carrollian noncommutative spacetimes are also obtained as the non-relativistic and ultra-relativistic limits of the κ-(A)dS noncommutative spacetime. These constructions allow us to analyze the non-trivial interplay between the quantum deformation parameter κ, the curvature parameter η and the speed of light parameter c.http://www.sciencedirect.com/science/article/pii/S0370269320302653Quantum groupsCarrollNewton–HookeAnti-de SitterKappa-deformationNoncommutative spaces |
| spellingShingle | Angel Ballesteros Giulia Gubitosi Ivan Gutierrez-Sagredo Francisco J. Herranz The κ-Newtonian and κ-Carrollian algebras and their noncommutative spacetimes Physics Letters B Quantum groups Carroll Newton–Hooke Anti-de Sitter Kappa-deformation Noncommutative spaces |
| title | The κ-Newtonian and κ-Carrollian algebras and their noncommutative spacetimes |
| title_full | The κ-Newtonian and κ-Carrollian algebras and their noncommutative spacetimes |
| title_fullStr | The κ-Newtonian and κ-Carrollian algebras and their noncommutative spacetimes |
| title_full_unstemmed | The κ-Newtonian and κ-Carrollian algebras and their noncommutative spacetimes |
| title_short | The κ-Newtonian and κ-Carrollian algebras and their noncommutative spacetimes |
| title_sort | κ newtonian and κ carrollian algebras and their noncommutative spacetimes |
| topic | Quantum groups Carroll Newton–Hooke Anti-de Sitter Kappa-deformation Noncommutative spaces |
| url | http://www.sciencedirect.com/science/article/pii/S0370269320302653 |
| work_keys_str_mv | AT angelballesteros theknewtonianandkcarrollianalgebrasandtheirnoncommutativespacetimes AT giuliagubitosi theknewtonianandkcarrollianalgebrasandtheirnoncommutativespacetimes AT ivangutierrezsagredo theknewtonianandkcarrollianalgebrasandtheirnoncommutativespacetimes AT franciscojherranz theknewtonianandkcarrollianalgebrasandtheirnoncommutativespacetimes AT angelballesteros knewtonianandkcarrollianalgebrasandtheirnoncommutativespacetimes AT giuliagubitosi knewtonianandkcarrollianalgebrasandtheirnoncommutativespacetimes AT ivangutierrezsagredo knewtonianandkcarrollianalgebrasandtheirnoncommutativespacetimes AT franciscojherranz knewtonianandkcarrollianalgebrasandtheirnoncommutativespacetimes |