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arXiv · 0709.4636

Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups

Benjamin Bahr·Thomas Thiemann
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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. 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.

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Benjamin Bahr, Thomas Thiemann. 2007-09-28. Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups. https://doi.org/10.1088/0264-9381%2F26%2F4%2F045012

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