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arXiv · gr-qc/9909053

Loop Quantum Gravity on Non-Compact Spaces

Matthias Arnsdorf·Sameer Gupta
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Abstract

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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Matthias Arnsdorf, Sameer Gupta. 2000-04-19. Loop Quantum Gravity on Non-Compact Spaces. https://doi.org/10.1016/s0550-3213(00)00196-6

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