Dynamical Quantum Geometry (DQG Programme)

Abstract

In this brief note (written as a lengthy letter), we describe the construction of a representation for the Weyl-algebra underlying Loop Quantum Geometry constructed from a diffeomorphism variant state, which corresponds to a ''condensate'' of Loop Quantum Geometry, resembling a static spatial geometry. We present the kinematical GNS-representation and the gauge- and diffeomorphism invariant Hilbert space representation and show that the expectation values of the geometric operators take essentialy classical values plus quantum corrections, which is similar to a ''local condensate'' of quantum geometry. We describe the idea for the construction of a scale dependent asymptotic map into a family of scale dependent lattice gauge theories, where scale separates the essential geometry and a low energy effective theory, which is described as degrees of freedom in the lattice gauge theory. If this idea can be implemented then it is likely to turn out that this Hilbert space contains in addition to gravity also gauge coupled ''extra degrees of freedom'', which may not be dynamically irrelevant.

19 pages, LaTeX, 3 figures

References in corpus (5)

• Discreteness of area and volume in quantum gravity
• Quantum Theory of Gravity I: Area Operators
• Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
• Reduction of a Quantum Theory
• Energy conditions outside a dielectric ball

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• Quantum cosmology from quantum gravity condensates: cosmological variables and lattice-refined dynamics
• Functional Renormalisation Group analysis of a Tensorial Group Field Theory on ${\mathbb{R}}^3$
• Generalized quantum gravity condensates for homogeneous geometries and cosmology
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Loop Quantum Gravity Vacuum with Nondegenerate Geometry
• From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
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• A Cosmological Sector in Loop Quantum Gravity
• Structural aspects of loop quantum gravity and loop quantum cosmology from an algebraic perspective
• Some notes on the Kodama state, maximal symmetry, and the isolated horizon boundary condition
• Dynamics in canonical models of loop quantum gravity
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• Towards Gaussian states for loop quantum gravity
• The kinematical Setup of Quantum Geometry: A Brief Review
• 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