COHERENT-STATE QUANTIZATION OF CONSTRAINT SYSTEMS

We study the quantization of systems with general first- and second-cl ass constraints from the point of view of coherent state phase-space p ath integration, and show that all such cases may be treated, within t he original classical phase space, by using suitable path-integral mea sures for the Lagrange multipliers which ensure that the quantum syste m satisfies the appropriate quantum constraint conditions. Unlike conv entional methods, our procedures involve no delta-functionals of the c lassical constraints, no need for dynamical gauge fixing of first-clas s constraints nor any average thereover, no need to eliminate second-c lass constraints, no potentially ambiguous determinants, as well as no need to add auxiliary dynamical variables expanding the phase space b eyond its original classical formulation, including no ghosts. Additio nally, our procedures have the virtue of resolving differences between suitable canonical and path-integral approaches, and thus agree with previous results obtained by other methods for such cases. Several exa mples are considered in detail. (C) 1997 Academic Press.