Equations for path mean values in non-Abelian gauge theory

The singularities in the functional equation for the simplest path Green's function $\displaystyle G(c)=\biggl<P\exp g\oint_c A\,dx\biggr>$ in non-Abelian gauge theory are studied in the framework of perturbation theory. It is shown that in the two-dimensional case $G(c)$ satisfies the equation $(\delta^2/\delta x_\mu^2(s)-m^4x^{\prime2}(s))G(c)=0$ for the wave functional of a relativistic string.