Gaugeinvariant coherent states for loop quantum gravity: II. NonAbelian gauge groups
Abstract
This is the second paper concerning gaugeinvariant 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 gaugeinvariant coherent states on certain special graphs by analytical and numerical methods. We find that their overlap is Gauss peaked in gaugeinvariant quantities, as long as states are not labeled by degenerate gauge orbits, i.e. points where the gaugeinvariant 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 gaugeinvariant phase space.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 February 2009
 DOI:
 10.1088/02649381/26/4/045012
 arXiv:
 arXiv:0709.4636
 Bibcode:
 2009CQGra..26d5012B
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 60 pages, 8 figures