On the geometry of relativistic anyon

A twistor model is proposed for the free relativistic anyon. The Hamiltonian reduction of this model by the action of the spin generator leads to the minimal covariant model; whereas that by the action of spin and mass generators leads to the anyon model with free phase space which is a cotangent bundle of the Lobachevsky plane with twisted symplectic structure. Quantum mechanics of that model is described by irreducible representations of the (2+1)-dimensional Poincare group.