Linear Differential Equations for a Fractional Spin Field

The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the SL(2, R) group. In the case of (2j + 1)-dimensional nonunitary representations of that group, 0 < 2j ∈ Z, they are transformed into equations for spin-j fields. A local gauge symmetry associated to the vector system of equations is identified and the simplest gauge invariant field action, leading to these equations, is constructed. 1 Revised version of the preprint DFTUZ/92/24, to be published in J. Math. Phys. e-mail: [email protected] e-mail: [email protected]