QUANTIZATION OF DYNAMIC-SYSTEMS WITH REDUCIBLE CONSTRAINTS AND THE SUPERPARTICLE

Abstract

Batalin-Fradkin-Vilkovisky-Becchi-Rouet-Stora-Tyutin quantization of dynamical systems, with irreducible first- and reducible second-class constraints satisfying some conditions, is performed by converting the second-class constraints into effective first-class ones. But restricting the phase space in an unusual way is necessary. A path integral is proposed by imposing some new second-class constraints to keep the original ones converted into effective first-class constraints. The new second-class constraints are reducible and the reducibility conditions include the new reducible first-class ones. The general definition of reducibility and the method of quantization are presented. In the light of these, a new set of covariant constraints for the massless Casalbuoni-Brink-Schwarz superparticle in 10 dimensions is proposed. Although the first- and second-class constraints of the new set are separated, they are infinitely reducible. Quantization of this dynamical system in a unitary gauge is given.