Quantization of first-class constraints with structure functions

As part of a program to desuperize BRST symmetries, we show how to translate the BRST construction completely in terms of standard symplectic geometry in the case where the constraints are derived from a foliation on a configuration space. The consequences of this approach on quantization are investigated. As a corollary, we solve (in a restricted setting) the problem of how to deal in quantization with (globally independent) first-class constraints with structure functions rather than structure constants. (orig.)