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

Bahr, Benjamin; Thiemann, Thomas

doi:10.1088/0264-9381/26/4/045012

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Gauge-invariant coherent states for loop quantum gravity: II. Non-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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Citation

Bahr, B., & Thiemann, T. (2009). Gauge-invariant coherent states for loop quantum gravity: II. Non-Abelian gauge groups. Classical and Quantum Gravity, 26(4): 045012. doi:10.1088/0264-9381/26/4/045012.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-451A-F

Abstract

This is the second paper concerning gauge-invariant coherent states for loop quantum gravity. Here, we deal with the gauge group SU(2), this being a significant complication compared to the Abelian U(1) case encountered in the previous article (Class. Quantum Grav. 26 045011). We study gauge-invariant coherent states on certain special graphs by analytical and numerical methods. We find that their overlap is Gauss peaked in gauge-invariant quantities, as long as states are not labeled by degenerate gauge orbits, i.e. points where the gauge-invariant configuration space has singularities. In these cases the overlaps are still concentrated around these points, but the peak profile exhibits a plateau structure. This shows how the semiclassical properties of the states are influenced by the geometry of the gauge-invariant phase space.