ANYON IN AN EXTERNAL ELECTROMAGNETIC-FIELD - HAMILTONIAN AND LAGRANGIAN FORMULATIONS

We propose a simple model for a free relativistic particle of fraction al 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 e xtended algebra, which is the first-class constraint, is obtained and gives the equation of motion of the anyon. In particular, from the lat ter it follows that the gyromagnetic ratio for a charged anyon is 2 du e to the parallelness of spin and momentum of the particle in 2+1 dime nsions. The canonical quantization is also considered.