Twisted Geometries Coherent States for Loop Quantum Gravity

TL;DR

This paper introduces a new family of coherent states for loop quantum gravity based on twisted geometry parametrization, showing improved peakedness properties and better disentanglement of holonomy actions compared to existing states.

Contribution

The paper develops a novel family of coherent states for loop quantum gravity inspired by twisted geometries, with enhanced peakedness and a new shift operator for holonomy analysis.

Findings

Similar area and holonomy features to heat-kernel states

Improved peakedness in flux direction

Effective disentanglement of holonomy actions

Abstract

We introduce a new family of coherent states for loop quantum gravity, inspired by the twisted geometry parametrization. We compute their peakedness properties and compare them with the heat-kernel coherent states. They show similar features for the area and the holonomy operators, but improved peakedness in the direction of the flux. At the gauge-invariant level, the new family is built from tensor products of coherent intertwiners. To study the peakedness of the holonomy operator, we introduce a new shift operator based on the harmonic oscillator representation associated with the twisted geometry parametrization. The new shift operator captures the components of the holonomy relevant to disentangle its action into a simple positive shift of the spins.