Planck-scale relativity from quantum $\kappa$-Poincar\'e algebra

TL;DR

This paper explores how quantum $ppa$-Poincare9 algebra modifies relativistic transformations at the Planck scale, revealing invariant Minkowski structure and saturated boosts, with implications for particle motion and relativistic effects.

Contribution

It extends the quantum $ppa$-Poincare9 algebra to the entire phase space and derives the covariant transformation properties of positions under deformed boosts.

Findings

Boosts leave the Minkowski metric invariant.

Boosts saturate at high velocities.

Time dilation and length contraction are analyzed in this framework.

Abstract

Extending the commutator algebra of quantum $\kappa$-Poincar\'e symmetry to the whole of the phase space, and assuming that this algebra is to be covariant under action of deformed Lorentz generators, we derive the transformation properties of positions under the action of deformed boosts. It turns out that these transformations leave invariant the quadratic form in the position space, which is the Minkowski metric and that the boosts saturate. The issues of massless and massive particles motion, as well as time dilatation and length contraction in this new framework are also studied.