Loop Quantum Gravity on Non-Compact Spaces

Details Loop Quantum Gravity on Non-Compact Spaces Loop Quantum Gravity on Non-Compact Spaces

1999-09-16

arxiv.org/abs/gr-qc/9909053v2

Nucl.Phys. B577 (2000) 529-546

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revised version, portions of the paper rearranged, references added

Scientific paper

10.1016/S0550-3213(00)00196-6

We present a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. Given any fixed background state representing a non-compact spatial geometry, we use the Gel'fand-Naimark-Segal construction to obtain a representation of the algebra of observables. The resulting Hilbert space can be interpreted as describing fluctuation of compact support around this background state. We also give an example of a state which approximates classical flat space and can be used as a background state for our construction.

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