I have a basic understanding of the Wightman axioms for QFT. I was reading the about the Mass Gap problem for simple compact gauge groups and was wondering how the gauge group is supposed to be implemented into the framework. The official problem description (pdf) says:
To establish existence of four-dimensional quantum gauge theory with gauge group $G$, one should define a quantum field theory (in the sense of the Wightman Axioms) with local quantum field operators in correspondence with the gauge invariant local polynomials in curvature and its covariant derivatives.
Can someone clarify what this means and what it means in terms of the physics?
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