Loop Quantum Gravity Vacuum with Nondegenerate Geometry

• Main Authors: Hanno Sahlmann, Tim Koslowski
• Format: Article
• Language: English
• Published: National Academy of Science of Ukraine 2012-05-01
• Series: Symmetry, Integrability and Geometry: Methods and Applications
• Subjects: loop quantum gravity; representations; geometric condensate
• Online Access: http://dx.doi.org/10.3842/SIGMA.2012.026

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.