Gauge-invariant coherent states for loop quantum gravity. II. Non-Abelian gauge groups
Oct, 2007
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Abstract: (arXiv)
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.- quantum gravity: loop space
- coherent state
- invariance: gauge
- gauge field theory: SU(2)
- Hilbert space
- kinematics
- geodesic
- numerical calculations
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