AN ALGEBRAIC EXTENSION OF DIRAC QUANTIZATION - EXAMPLES

An extension of the Dirac procedure for the quantization of constraine d systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especi ally in the context of nonlinear, diffeomorphism invariant theories su ch as general relativity. Recently, an extension of the required type was proposed using algebraic quantization methods. In this paper, the key conceptual and technical aspects of the algebraic program are illu strated through a number of finite dimensional examples. The choice of examples and some of the analysis is motivated by certain peculiar pr oblems endemic to quantum gravity. However, prior knowledge of general relativity is not assumed in the main discussion. Indeed, the methods introduced and conclusions arrived at are applicable to any system wi th first class constraints. In particular, they resolve certain techni cal issues which are present also in the reduced phase space approach to quantization of these systems. (C) 1994 American Institute of Physi cs.