Gaussian averaging versus group averaging for noncompact gauge groups

Determine whether the Gaussian average over exterior matter states is superfluous for tensor networks with non-compact gauge groups, or whether it supplies an independent operation beyond the renormalizing group average implemented by the operator-valued weight.

Background

The paper uses a Gaussian ensemble of matter states to obtain minimization over generalized entropies and to model ignorance of exterior matter. The authors observe that the Gaussian ensemble average and the operator-valued weight implementing group averaging both define maps from the full bounded-operator algebra to the gauge-invariant algebra.

This raises an unresolved question about whether randomness is an additional physical assumption or is already effectively generated by gauge averaging, particularly for noncompact gauge groups.