WEAK DIRAC BRACKET CONSTRUCTION AND THE SUPERPARTICLE COVARIANT QUANTIZATION PROBLEM

The general procedure for constructing a consistent covariant Dirac-ty pe bracket for the models with mixed first and second class constraint s is presented. The proposed scheme essentially relies upon explicit s eparation of the initial constraints into infinitely reducible first a nd second class ones (by making use of some covariant projectors). Red ucibility of the second class constraints involved manifests itself in weakening some properties of the bracket as compared to the standard Dirac one. In particular, a commutation of any quantity with the secon d class constraints and the Jacobi identity holds on the second class constraints surface only. The procedure developed is realized for a N = 1 Brink-Schwarz superparticle in arbitrary dimension and for a N = 1 , D = 9 massive superparticle with the Wess-Zumino term. The possibili ty to apply the bracket for quantizing the superparticles within the f ramework of the recent unified algebra approach by Batalin and Tyutin [20-22] is examined. It is shown, in particular, that for a D = 9 mass ive superparticle it is impossible to construct a Dirac-type bracket p ossessing a (strong) Jacobi identity in a full phase space.