A functional equation for exponential loop integrals in gauge theories

We analyze the behavior of the operator ψ(Γ) = TrP _Γexp(∲A· dx) 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.