A geometric procedure for the reduced-state-space quantisation of constrained systems

We propose in this paper a new method for the quantisation of systems with first-class constraints. This method is a combination of the coherent-state-path-integral quantisation developed by Klauder, with the ideas of reduced state space quantisation. The key idea is that the physical Hilbert space may be defined by a coherent-state path-integral on the reduced state space and that the metric on the reduced state space that is necessary for the regularisation of the path-integral may be computed from the geometry of the classical reduction procedure. We provide a number of examples–notably the relativistic particle. Finally we discuss the quantisation of systems, whose reduced state space has orbifold-like singularities.