Phys. Rev. D 62, 064030 (2000) [6 pages]Classical geometry from a physical state in canonical quantum gravityReceived 21 April 2000; published 28 August 2000 We construct a weave state which approximates a degenerate three-metric of rank 2 at large scales. It turns out that a nondegenerate metric region can be evolved from this degenerate metric by the classical Ashtekar equations; hence, the degeneracy of the three-metrics is not preserved by the evolution of Ashtekar’s equations. As the s-knot state corresponding to this weave is shown to solve all the quantum constraints in loop quantum gravity, a physical state in canonical quantum gravity is related to the familiar classical geometry. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.62.064030
DOI:
10.1103/PhysRevD.62.064030
PACS:
04.60.-m, 04.20.Cv, 04.20.Fy
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