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Journal Article

Gauge-invariant coherent states for loop quantum gravity: I. Abelian gauge groups

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Bahr,  Benjamin
Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Thiemann,  Thomas
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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cqg9_4_045011.pdf
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Citation

Bahr, B., & Thiemann, T. (2009). Gauge-invariant coherent states for loop quantum gravity: I. Abelian gauge groups. Classical and Quantum Gravity, 26(4): 045011. doi:10.1088/0264-9381/26/4/045011.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-451E-7
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 defined by Thiemann and Winkler to the gauge-invariant Hilbert space. This being the first step toward constructing physical coherent states, we arrive at a set of gauge-invariant states that approximate well the gauge-invariant degrees of freedom of Abelian loop quantum gravity (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. In a companion paper, we will turn to the more sophisticated case of SU(2).