Dynamical Quantum Geometry (DQG Programme)

TL;DR

This paper constructs a representation in Loop Quantum Geometry resembling a static spatial geometry, showing classical-like expectation values and proposing a scale-dependent approach for effective low-energy theories.

Contribution

It introduces a new representation based on a diffeomorphism variant state, resembling a condensate, and discusses a scale-dependent framework for quantum geometry and gauge theories.

Findings

Expectation values of geometric operators are essentially classical with quantum corrections.

The representation resembles a static spatial geometry, akin to a condensate.

A proposed scale-dependent map links quantum geometry to lattice gauge theories.

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.