kappa-Minkowski spacetime as the result of Jordanian twist deformation

TL;DR

This paper compares two methods of deriving kappa-Minkowski spacetime using Abelian and Jordanian twists, revealing new dispersion relations and connecting algebraic approaches with physical models.

Contribution

It introduces a novel extension of deformed Lorentz algebra via Jordanian twists and relates it to the Hopf algebra approach, deriving new dispersion relations.

Findings

Jordanian twists yield new energy-dependent dispersion relations.

Both algebraic approaches are shown to be equivalent.

Kappa-Minkowski spacetime can be derived from different twist deformations.

Abstract

Two one-parameter families of twists providing kappa-Minkowski * -product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. The first one is the Hopf module algebra point of view, which is strictly related with Drinfeld's twisting tensor technique. The other one relies on an appropriate extension of "deformed realizations" of nondeformed Lorentz algebra by the quantum Minkowski algebra. This extension turns out to be de Sitter Lie algebra. We show the way both approaches are related. The second path allows us to calculate deformed dispersion relations for toy models ensuing from different twist parameters. In the Abelian case one recovers kappa-Poincar'e dispersion relations having numerous applications in doubly special relativity. Jordanian twists provide a new type of dispersion relations which in the minimal case (related to Weyl-Poincar'e algebra) takes an energy-dependent linear mass deformation form.