Free Relativistic Anyons 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 $\left\{ S_\mu , S_\nu \right\}\,=\,\epsilon_{\mu \nu \gamma}S^\gamma$. It is shown that it is a general consequence of these features that the Poincar\`e 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.