Relativstic particle dynamics in D=2+1

Abstract

We propose a SUSY variant of the action for a massless spinning particles via the inclusion of twistor variables. The action is constructed to be invariant under SUSY transformations and -reparametrizations even when an interaction field is including. The constraint analysis is achieved and the equations of motion are derived. The commutation relations obtained for the commuting spinor variables show that the particle states have fractional statistics and spin. At once we introduce a possible massive term for the non-interacting model.