Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 026, 15 pages      arXiv:1109.4688      https://doi.org/10.3842/SIGMA.2012.026
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

Loop Quantum Gravity Vacuum with Nondegenerate Geometry

Tim Koslowski a and Hanno Sahlmann b
a) Perimeter Institute for Theoretical Physics, Waterloo, Canada
b) APCTP, and Physics Department of POSTECH University, Pohang, Korea

Received September 23, 2011, in final form May 03, 2012; Published online May 12, 2012

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.

Key words: loop quantum gravity; representations, geometric condensate.

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