Linear differential equations for a fractional spin field

Source abstract

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.