Geometric interpretation of Planck-scale-deformed co-products

TL;DR

This paper introduces a geometric framework for understanding interactions in theories with maximally symmetric momentum spaces, unifying known composition laws and suggesting new models with anti-de Sitter geometry.

Contribution

It provides a general characterization of interaction descriptions using the isometry group of momentum space, encompassing known models and enabling future model development.

Findings

Known composition laws satisfy the proposed condition

Framework unifies different models of momentum space interactions

Suggests potential for new models with anti-de Sitter geometry

Abstract

For theories formulated with a maximally symmetric momentum space we propose a general characterization for the description of interactions in terms of the isometry group of the momentum space. The well known cases of $\kappa$-Poincar\'e-inspired and (2+1)-dimensional gravity-inspired composition laws both satisfy our condition. Future applications might include the proposal of a class of models based on momenta spaces with anti-de Sitter geometry.