  Gauge invariant quark two-point Green's functions defined with path-ordered
gluon field phase factors along skew-polygonal lines joining the quark to the
antiquark are considered. Functional relations between Green's functions with
different numbers of path segments are established. An integral equation is
obtained for the Green's function defined with a phase factor along a single
straight line. The equation implicates an infinite series of two-point Green's
functions, having an increasing number of path segments; the related kernels
involve Wilson loops with contours corresponding to the skew-polygonal lines of
the accompanying Green's function and with functional derivatives along the
sides of the contours. The series can be viewed as an expansion in terms of the
global number of the functional derivatives of the Wilson loops. The
lowest-order kernel, which involves a Wilson loop with two functional
derivatives, provides the framework for an approximate resolution of the
equation.
