QUANTIZATION AND BOSONIC BRST THEORY

We show that BRST symmetry has a natural bosonic analogue in symplectic geometry. In fact, bosonic BRST theory arises as a purely symplectic construction, which can naturally be viewed as a specific instance of symplectic induction. In this context, both the BRST charge and the total ghost number appear as the "components" of a momentum map on an extended symplectic phase space. Our approach to bosonic BRST theory is motivated by certain problems which arise in the quantization of constrained classical systems. We show that the usual Dirac quantization prescription is incorrect when the system has nonunimodular symmetries and demonstrate how bosonic BRST theory may be used to rectify this. As a byproduct we also prove, under certain circumstances, that both the processes of induction and reduction commute with quantization. © 1991.