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

Charis Anastopoulos
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Abstract

We propose in this paper an alternative 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.

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Charis Anastopoulos. 2004-11-27. A geometric procedure for the reduced-state-space quantisation of constrained systems. https://arxiv.org/abs/gr-qc/0411130

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