These questions are sort of a continuation of this previous question.
I would like to know of the proof/reference to the fact that in a pure gauge theory Wilson loops are all the possible gauge invariant operators (... that apparently even the local operators can be gotten from the not-so-obviously-well-defined infinitesimal loop limit of them!..)
If the pure gauge theory moves into a confining phase then shouldn't there be more observables than just the Wilson loops... like "glue balls" etc? Or are they also somehow captured by Wilson loops?
If matter is coupled to the gauge theory are the so called ``chiral primary" operators, $Tr[\Phi_{i1}\Phi_{i2}\cdots\Phi_{im}]$ a separate class of observables than either the baryons or mesons (for those field which occur in the fundmanetal and the anti-fundamental of the gauge group) or Wilson loops?..is there a complete classification of all observables in the confined phase?
{..like as I was saying last time..isn't the above classification the same thing as what in Geometric Invariant Theory is well studied as asking for all G-invariant polynomials in a polynomial ring (..often mapped to $\mathbb{C}^n$ for some $n$..) for some group $G$?..)
But can there be gauge invariant (and hence colour singlet?) operators which are exponential in the matter fields?
In the context of having new colour singlet( or equivalently gauge invariant?) observables in the confining phase I would like to ask the following - if one is working on a compact space-(time?) then does the Gauss's law (equation of motion for $A_0$) somehow enforce the colour-singlet/confinement condition on the matter observables?..hence possibly unlike on flat space-time, here even at zero gauge coupling one still has to keep track of the confinement constraint?
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