Loop Quantum Gravity Vacuum with Nondegenerate Geometry

TL;DR

This paper explores the construction of non-degenerate geometric vacuum states in loop quantum gravity, which could enhance understanding of quantum spacetime and inform effective theories and cosmological models.

Contribution

It introduces methods to construct non-degenerate geometric vacuum states within loop quantum gravity frameworks, expanding the scope beyond degenerate geometries.

Findings

Constructed non-degenerate vacuum states for Lie and Weyl algebras

Potential applications in Loop Quantum Cosmology and effective field theories

Provides a foundation for further generalizations in quantum gravity

Abstract

In loop quantum gravity, states of the gravitational field turn out to be excitations over a vacuum state that is sharply peaked on a degenerate spatial geometry. While this vacuum is singled out as fundamental due to its invariance properties, it is also important to consider states that describe non-degenerate geometries. Such states have features of Bose condensate ground states. We discuss their construction for the Lie algebra as well as the Weyl algebra setting, and point out possible applications in effective field theory, Loop Quantum Cosmology, as well as further generalizations.