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Consider the non-abelian phase factor around a closed path $C$, $$\psi(C) = \mathrm{P} e^{\oint A_\mu dx^\mu} = \mathrm{P} e^{\int_0^{2\pi} dt \, A_\nu(x(t)) \dot{x}^\nu(t) }$$ Let us take the functional derivative with respect to $x^\mu(s)$ \begin{align} \frac{\delta}{\delta x^\mu(s)} \psi(C) %& = \int_0^{2\pi} dt \, ...