Classical Geometry from a Physical State in Canonical Quantum Gravity

Abstract

We construct a weave state which approximates a degenerate 3-metric of rank 2 at large scales. It turns out that a non-degenerate metric region can be evolved from this degenerate metric by the classical Ashtekar equations, hence the degeneracy of 3-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.

Corrected typos, updated references

References in corpus (4)

• Loop Quantum Gravity on Non-Compact Spaces
• $\hat{Q}$ operator for canonical quantum gravity
• Causal structure and degenerate phase boundaries
• On the degenerate phase boundaries

Cited by in corpus (6)

• Fundamental Structure of Loop Quantum Gravity
• Statistical geometry of random weave states
• $\hat{Q}$ operator for canonical quantum gravity
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Quantization of static space-times
• Quantum Dyanmics of Loop Quantum Gravity