Anyon in an external electromagnetic field: Hamiltonian and Lagrangian formulations

We propose a simple model for a free relativistic particle of fractional spin in 2+1 dimensions. Using the Hamiltonian formulation with the set of constraints, we introduce the electromagnetic interaction of a charged anyon and obtain the Lagrangian. The Casimir operator of the extended algebra, which is the first-class constraint, is obtained and gives the equation of motion of the anyon. In particular, from the latter it follows that the gyromagnetic ratio for a charged anyon is two due to the parallelness of spin and momentum of the particle in 2+1 dimensions. The canonical quantization is also considered.