Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-04-26
Class.Quant.Grav. 23 (2006) 5547-5586
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
51 pages, LaTeX, no figures, revised version
Scientific paper
10.1088/0264-9381/23/18/005
We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer variables. The quantization, in our formulation, amounts to introducing the `quantum' polymer *-star algebra and looking for positive linear functionals, called states. Assumed in our paper homeomorphism invariance allows to derive the complete class of the states. They are determined by the homeomorphism invariant states defined on the CW-complex *-algebra. The corresponding GNS representations of the polymer *-algebra and their self-adjoint extensions are derived, the equivalence classes are found and invariant subspaces characterized. In the preceding letter (the part I) we outlined those results. Here, we present the technical details.
Kaminski Wojciech
Lewandowski Jerzy
Okolow Andrzej
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