The noncommutative space of light-like worldlines

Abstract

The noncommutative space of light-like worldlines that is covariant under the light-like (or null-plane) $\kappa$-deformation of the (3+1) Poincaré group is fully constructed as the quantization of the corresponding Poisson homogeneous space of null geodesics. This new noncommutative space of geodesics is five-dimensional, and turns out to be defined as a quadratic algebra that can be mapped to a non-central extension of the direct sum of two Heisenberg-Weyl algebras whose noncommutative parameter is just the Planck scale parameter ${\kappa }^{-1}$. Moreover, it is shown that the usual time-like $\kappa$-deformation of the Poincaré group does not allow the construction of the Poisson homogeneous space of light-like worldlines. Therefore, the most natural choice in order to model the propagation of massless particles on a quantum Minkowski spacetime seems to be provided by the light-like $\kappa$-deformation.

16 pages. Minor corrections

References in corpus (6)

• kappa-Minkowski spacetime as the result of Jordanian twist deformation
• The kappa-(A)dS quantum algebra in (3+1) dimensions
• The $\kappa$-(A)dS noncommutative spacetime
• Noncommutative spaces of worldlines
• Canonical and Lie-algebraic twist deformations of $\kappa$-Poincare and contractions to $\kappa$-Galilei algebras
• Cayley-Klein Lie bialgebras: Noncommutative spaces, Drinfel'd doubles and kinematical applications

Cited by in corpus (1)

• All noncommutative spaces of $\kappa$-Poincaré geodesics