Loop Quantum Gravity on Non-Compact Spaces

Preprint

17 September 1999

preprint
Published by arXiv in arXiv

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.

Keywords

LOOP QUANTUM GRAVITY
BACKGROUND STATE
QUANTUM GRAVITY
COMPACT SPACES
HILBERT SPACE
ALGEBRA

All Related Versions

Version 1, 1999-09-17, ArXiv
Version 2, 2000-04-19, ArXiv
Published version: Nuclear Physics B, 577 (3), 529.

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