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

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

2007-09-28

arxiv.org/abs/0709.4619v1

Class.Quant.Grav.26:045011,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

36 pages

Scientific paper

10.1088/0264-9381/26/4/045011

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.

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