  We propose a simple model for a free relativistic particle of fractional spin
in 2+1 dimensions which satisfies all the necessary conditions. The canonical
quantization of the system leads to the description of one- particle states of
the Poincare group with arbitrary spin. Using the Hamil- tonian formulation
with the set of constraints, we introduce the electro- magnetic 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 in this case.

High Energy Physics - Theory