On loop quantum gravity kinematics with non-degenerate spatial background

Abstract

In a remarkable paper, T. Koslowski introduced kinematical representations for loop quantum gravity in which there is a non-degenerate spatial background metric present. He also considered their properties, and showed that Gauss and diffeomorphism constraints can be implemented. With the present article, we streamline and extend his treatment. In particular, we show that the standard regularization of the geometric operators leads to well defined operators in the new representations, and we work out their properties fully. We also give details on the implementation of the constraints. All of this is done in such a way as to show that the standard representation is a particular (and in some ways exceptional) case of the more general constructions. This does not mean that these new representations are as fundamental as the standard one. Rather, we believe they might be useful to find some form of effective theory of loop quantum gravity on large scales.

13 pages, 2 figures. v2: Some clarifications added, typos removed. Virtually identical with published version

References in corpus (7)

• Background Independent Quantum Gravity: A Status Report
• Discreteness of area and volume in quantum gravity
• Quantum Theory of Gravity I: Area Operators
• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
• Representations of the Weyl Algebra in Quantum Geometry
• Dynamical Quantum Geometry (DQG Programme)
• Towards new background independent representations for Loop Quantum Gravity

Cited by in corpus (23)

• Quantum Cosmology from Group Field Theory Condensates: a Review
• A new vacuum for Loop Quantum Gravity
• Towards classical geometrodynamics from Group Field Theory hydrodynamics
• Quantum gravity kinematics from extended TQFTs
• On entanglement entropy in non-Abelian lattice gauge theory and 3D quantum gravity
• Loop Quantum Gravity Vacuum with Nondegenerate Geometry
• Flux formulation of loop quantum gravity: Classical framework
• Loop quantum gravity coupled to a scalar field
• The generator of spatial diffeomorphisms in the Koslowski- Sahlmann representation
• The Koslowski-Sahlmann representation: Quantum Configuration Space
• A Brief Overview of Results about Uniqueness of the Quantization in Cosmology
• The Koslowski- Sahlmann representation: Gauge and diffeomorphism invariance
• A new realization of quantum geometry
• Structural aspects of loop quantum gravity and loop quantum cosmology from an algebraic perspective
• Quantum geometry with a nondegenerate vacuum: a toy model
• Dynamics in canonical models of loop quantum gravity
• A quantum kinematics for asymptotically flat spacetimes
• Positive energy in quantum gravity
• Towards Gaussian states for loop quantum gravity
• Asymptotic Flatness and Quantum Geometry
• A note on conformally compactified connection dynamics tailored for anti-de Sitter space
• Abelian 2+1D Loop Quantum Gravity Coupled to a Scalar Field
• New insights in quantum geometry