A Uniqueness Theorem for Constraint Quantization

Abstract

This work addresses certain ambiguities in the Dirac approach to constrained systems. Specifically, we investigate the space of so-called ``rigging maps'' associated with Refined Algebraic Quantization, a particular realization of the Dirac scheme. Our main result is to provide a condition under which the rigging map is unique, in which case we also show that it is given by group averaging techniques. Our results comprise all cases where the gauge group is a finite-dimensional Lie group.

23 pages, RevTeX, further comments and references added (May 26. '99)

References in corpus (6)

• Loop Quantum Gravity
• On the Generality of Refined Algebraic Quantization
• Canonical and path integral quantisation of string cosmology models
• The Quantum Modular Group in (2+1)-Dimensional Gravity
• Product Representations and the Quantization of Constrained Systems
• Coherent State Path Integrals at (Nearly) 40

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