THE PARASUPERSYMMETRIC SPINNING PARTICLE AND TOPOLOGICAL GAUGE FIELDS

Abstract

The first quantization of the D-dimensional relativistic spinning particle with the action invariant under reparametrizations and local worldline parasupersymmetric transformations is performed. The corresponding symmetry algebra is not of the Lie kind and is known as a polynomial algebra. It is found that the physical space of the massless particle is described by the strength tensors of Abelian antisymmetric gauge fields and topological gauge fields. In the special case D = 3 the Abelian Chern–Simons gauge field appears as a wave function of the particle. The generalizations to a massive parasupersymmetric spinning particle are presented.