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

Understand

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.