A free relativistic anyon with canonical spin algebra

We discuss a relativistic free particle with fractional spin in 2+1 dimensions, where the dual spin components satisfy the canonical angular momentum algebra {Sμ, Sν} = ϵμνγSγ. It is shown that it is a general consequence of these features that the Poincaré invariance is broken down to the Lorentz one, so indicating that it is not possible to keep simultaneously the free nature of the anyon and the translational invariance.