Abstract

We show that the reduction of a planar free spin-1/2 particle system by the constraint fixing its total angular momentum produces the one-dimensional Akulov-Pashnev-Fubini-Rabinovici superconformal mechanics model with the nontrivially coupled boson and fermion degrees of freedom. The modification of the constraint by including the particle's spin with the relative weight n ? ?, n > 1, and subsequent application of the Dirac reduction procedure ('first quantize and then reduce') give rise to the anomaly free quantum system with the order n nonlinear superconformal symmetry constructed recently by Leiva and Plyushchay [hep-th/0304257]. We establish the origin of the quantum corrections to the integrals of motion generating the nonlinear superconformal algebra, and fix completely its form. © 2003 Elsevier B.V. All rights reserved.