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This is the second paper concerning gauge-invariant coherent states for LoopQuantum Gravity. Here, we deal with the gauge group SU(2), this being asignificant complication compared to the abelian U(1) case encountered in theprevious article. We study gauge-invariant coherent states on certain specialgraphs by analytical and numerical methods. We find that their overlap isGauss-peaked in gauge-invariant quantities, as long as states are not labeledby degenerate gauge orbits, i.e. points where the gauge-invariant configurationspace has singularities. In these cases the overlaps are still concentratedaround these points, but the peak profile exhibits a plateau structure. Thisshows how the semiclassical properties of the states are influenced by thegeometry of the gauge-invariant phase space.

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