A PSEUDOCLASSICAL MODEL FOR P,T-INVARIANT PLANAR FERMIONS

A pseudoclassical model is proposed for the description of planar P,T- invariant massive fermions. The quantization of the model leads to the (2+1)-dimensional P,T-invariant fermion model used recently in P,T-co nserving theories of high-T-c superconductors. The rich symmetry of th e quantum model is elucidated through the analysis of the canonical st ructure of its pseudoclassical counterpart. We show that both the quan tum P,T-invariant planar massive fermion model and the proposed pseudo classical model - for a particular choice of the parameter appearing i n the Lagrangian - have a U(1,1) dynamical symmetry as well as an N = 3 supersymmetry. The hidden supersymmetry leads to a nonstandard super extension of the (2+1)-dimensional Poincare group. In the quantum theo ry the one-particle states provide an irreducible representation of th e extended supergroup labelled by the zero eigenvalue of the superspin . We discuss the gauge modification of the pseudoclassical model and c ompare our results with those obtained from the standard pseudoclassic al model for massive planar fermions.