Noncommutative spaces of worldlines
Abstract
The space of timelike geodesics on Minkowski spacetime is constructed as a coset space of the Poincaré group in (3+1) dimensions with respect to the stabilizer of a worldline. When this homogeneous space is endowed with a Poisson homogeneous structure compatible with a given PoissonLie Poincaré group, the quantization of this Poisson bracket gives rise to a noncommutative space of worldlines with quantum group invariance. As an oustanding example, the Poisson homogeneous space of worldlines coming from the κPoincaré deformation is explicitly constructed, and shown to define a symplectic structure on the space of worldlines. Therefore, the quantum space of κPoincaré worldlines is just the direct product of three HeisenbergWeyl algebras in which the parameter κ^{1} plays the very same role as the Planck constant ħ in quantum mechanics. In this way, noncommutative spaces of worldlines are shown to provide a new suitable and fully explicit arena for the description of quantum observers with quantum group symmetry.
 Publication:

Physics Letters B
 Pub Date:
 May 2019
 DOI:
 10.1016/j.physletb.2019.03.029
 arXiv:
 arXiv:1902.09132
 Bibcode:
 2019PhLB..792..175B
 Keywords:

 Timelike worldlines;
 Quantum groups;
 Poisson homogeneous spaces;
 Kappadeformation;
 Noncommutative spaces;
 Quantum observers;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 15 pages