In this paper the author shows that holonomies on Wilson loops are useful tools in GR. I have no problem with the gauge invariance on these loops which comes from the cyclicity of thr trace.(adsbygoogle = window.adsbygoogle || []).push({});

Bonzom writes then:

We are moreover interested in SU(2) gauge invariant states. Gauge transformations act on holonomies only on their endpoints. If h is a map from Σ to SU(2), then the holonomy transforms as

##U_e (A^h ) = h(t(e))U_e (A)h(s(e))^{−1} ##, with t(e), s(e) being respectively the source and target points of the path e. When focusing on a single graph Γ, this reduces gauge transformations

to an action of SU(2)^V on the set of cylindrical functions over Γ. So from any function f over SU(2)^E , one gets an invariant function by averaging over the SU(2)^V action.

Here we have edges and vertices.What is this averaging over the action ar the nodes?

Thanks for your help.

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# A Averaging holonomies

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