Exploring the diffeomorphism invariant Hilbert space of a scalar field

Details Exploring the diffeomorphism invariant Hilbert space of a scalar field Exploring the diffeomorphism invariant Hilbert space of a scalar field

2006-09-08

arxiv.org/abs/gr-qc/0609032v3

Class.Quant.Grav.24:4601-4616,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, no figures; v3: corrected typos, added reference, some clarifications added; version as published in CQG

Scientific paper

10.1088/0264-9381/24/18/003

As a toy model for the implementation of the diffeomorphism constraint, the interpretation of the resulting states, and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism invariant states for a scalar field. We give a very explicit formula for the scalar product on this space, and discuss its structure. Then we turn to the quantization of a certain class of diffeomorphism invariant quantities on that space, and discuss in detail the ordering issues involved. On a technical level these issues bear some similarity to those encountered in full loop quantum gravity.

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