Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups

TL;DR

This paper constructs gauge-invariant coherent states for Abelian Loop Quantum Gravity by projecting complexifier states, resulting in states that approximate gauge-invariant degrees of freedom and encode graph topology with good peakedness properties.

Contribution

It introduces a method to obtain gauge-invariant coherent states in Abelian LQG by projection, preserving peakedness and encoding graph topology.

Findings

States approximate gauge-invariant degrees of freedom.

States encode explicit graph topology information.

States exhibit peakedness properties similar to gauge-variant states.

Abstract

In this paper we investigate the properties of gauge-invariant coherent states for Loop Quantum Gravity, for the gauge group U(1). This is done by projecting the corresponding complexifier coherent states, which have been applied in numerous occasions to investigate the semiclassical limit of the kinematical sector, to the gauge-invariant Hilbert space. This being the first step to construct physical coherent states, we arrive at a set of gauge-invariant states that approximate well the gauge-invariant degrees of freedom of abelian LQG. Furthermore, these states turn out to encode explicit information about the graph topology, and show the same pleasant peakedness properties known from the gauge-variant complexifier coherent states.