Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
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.
Cite
@article{arxiv.0709.4636,
title = {Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups},
author = {Benjamin Bahr and Thomas Thiemann},
journal= {arXiv preprint arXiv:0709.4636},
year = {2009}
}
Comments
60 pages, 8 figures