ON GUPTA-BLEULER QUANTIZATION OF SYSTEMS WITH SECOND-CLASS CONSTRAINTS

Abstract

In this paper we discuss Hamiltonian systems with mixed first- and second-class constraints. We prove on classical level that in a neighborhood of the constraint surface the complexified constraints can always be split into a holomorphic and an antiholomorphic set. This is a necessary condition for implementing the holomorphic set consistently on the ket-states of the corresponding quantum theory. The quantization is performed with BRST-methods using a non-Hermitian BRST-operator. As an example we use this method to quantize the four-dimensional superparticle.