The model of a free relativistic particle with fractional spin

The model of a free relativistic particle with fractional spin in 2+1 dimensions is proposed. It is shown that there are two schemes of the canonical quantization of the model. One of these leads to the description of the physical states of the model as one-particle states of a (2+1)-dimensional Poincare group either by multi-valued functions in the case of a standard realization of canonical coordinates and momenta operators, or by single-valued functions in the case of a nonstandard realization of these operators. The second scheme leads to a (2+1)-dimensional analog of an infinite-component Majorana equation and to a mass shell condition as quantum conditions on the physical state vectors. Two variants of action for a free field with arbitrary (fractional) spin are constructed on the basis of these quantum conditions. 31 refs