Coherent State Quantization of Constraint Systems

We study the quantization of systems with general first- and second-class constraints from the point of view of coherent state phase-space path integration, and show that all such cases may be treated, within the original classical phase space, by using suitable path-integral measures for the Lagrange multipliers which ensure that the quantum system satisfies the appropriate quantum constraint conditions. Unlike conventional methods, our procedures involve noδ-functionals of the classical constraints, no need for dynamical gauge fixing of first-class constraints nor any average thereover, no need to eliminate second-class constraints, no potentially ambiguous determinants, as well as no need to add auxiliary dynamical variables expanding the phase space beyond its original classical formulation, including no ghosts. Additionally, 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 examples are considered in detail.