Colourful Poincar\'e symmetry, gravity and particle actions

TL;DR

This paper extends the three-dimensional Poincaré algebra to include a colour symmetry, enabling the formulation of coloured Poincaré gravity and generalized particle models, advancing the understanding of particles in non-abelian backgrounds.

Contribution

It introduces a coloured Poincaré algebra in 3D, facilitating new gravity models and particle actions with non-abelian symmetry considerations.

Findings

Constructed a coloured Poincaré algebra in 3D

Developed coloured Poincaré gravity models

Presented generalized particle models with different symmetry orbits

Abstract

We construct a generalisation of the three-dimensional Poincar\'e algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincar\'e gravity in three space-time dimensions as well as to study generalisations of massive and massless free particle models. We present various such generalised particle models that differ in which orbits of the coloured Poincar\'e symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a non-abelian background field or as a starting point for a worldline formulation of an associated quantum field theory.