On the Generality of Refined Algebraic Quantization

Details On the Generality of Refined Algebraic Quantization On the Generality of Refined Algebraic Quantization

1998-12-07

arxiv.org/abs/gr-qc/9812024v2

Class.Quant.Grav.16:2479-2488,1999

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, no figures, ReVTeX, some changes in presentation, some references added

Scientific paper

10.1088/0264-9381/16/7/321

The Dirac quantization `procedure' for constrained systems is well known to have many subtleties and ambiguities. Within this ill-defined framework, we explore the generality of a particular interpretation of the Dirac procedure known as refined algebraic quantization. We find technical conditions under which refined algebraic quantization can reproduce the general implementation of the Dirac scheme for systems whose constraints form a Lie algebra with structure constants. The main result is that, under appropriate conditions, the choice of an inner product on the physical states is equivalent to the choice of a ``rigging map'' in refined algebraic quantization.

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