Colourful Poincare symmetry, gravity and particle actions

We construct a generalisation of the three-dimensional Poincare algebra that also includes a colour symmetry factor. This algebra can be used to define coloured Poincare 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 Poincare symmetry are described. Our approach can be seen as a stepping stone towards the description of particles interacting with a nonabelian background field or as a starting point for a worldline formulation of an associated quantum field theory.

Automated summary

The paper presents a generalization of the three-dimensional Poincare algebra that includes a color symmetry factor, which can be used to define colored Poincare gravity and study generalized particle models. Different particle models based on colored Poincare symmetry orbits are discussed, serving as a starting point for describing particles interacting with a nonabelian background field or as a worldline formulation for associated quantum field theory.