On Little Groups and Boosts of $\kappa$-deformed Poincare Group

TL;DR

This paper extends Wigner's little group approach to the $$-deformed Poincare9 group, deriving deformed Lorentz transformations and discussing potential experimental deviations at high energies.

Contribution

It generalizes the representation theory of the Poincare9 group to the $$-deformed case and derives associated Lorentz transformations.

Findings

Deformed Lorentz transformations of energy and momentum are derived.

Potential experimental deviations from standard Poincare9 predictions at high energies.

Framework suggests observable effects if $$-deformed symmetry is fundamental.

Abstract

We show how Wigner's little group approach to the representation theory of Poincar\'e group may be generalized to the case of $\kappa$-deformed Poincar\'e group. We also derive the deformed Lorentz transformations of energy and momentum. We find that if the $\kappa$-deformed Poincar\'e group is adopted as the fundamental symmetry of nature, it results in deviations from predictions of the Poincar\'e symmetry at large energies, which may be experimentally observable.