Colourful Poincar\'e symmetry, gravity and particle actions

Understand

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.