Noncanonical quantization of gravity. II. Constraints and the physical Hilbert space

Details Noncanonical quantization of gravity. II. Constraints and the physical Hilbert space Noncanonical quantization of gravity. II. Constraints and the physical Hilbert space

2001-02-09

arxiv.org/abs/gr-qc/0102041v1

J.Math.Phys. 42 (2001) 4440-4465

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 42 pages, no figures

Scientific paper

10.1063/1.1385375

The program of quantizing the gravitational field with the help of affine field variables is continued. For completeness, a review of the selection criteria that singles out the affine fields, the alternative treatment of constraints, and the choice of the initial (before imposition of the constraints) ultralocal representation of the field operators is initially presented. As analogous examples demonstrate, the introduction and enforcement of the gravitational constraints will cause sufficient changes in the operator representations so that all vestiges of the initial ultralocal field operator representation disappear. To achieve this introduction and enforcement of the constraints, a well characterized phase space functional integral representation for the reproducing kernel of a suitably regularized physical Hilbert space is developed and extensively analyzed.

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