A functional equation for exponential loop integrals in gauge theories

We analyze the behavior of the operator $\text{ψ(Γ) =}\text{Tr}\text{P}{}_{\mathrm{\Gamma }}\text{exp}\text{(?A·}\text{d}\text{x)}$ under variation of the entire closed contour Γ. An equation for the second contour variation ofψ (Γ) is derived. It codes the dynamics of the gauge theory in a gauge-invariant and frame-independent way, without reference to the connection.