Polygonal lines are used for the paths of the gluon field phase factors
entering in the definition of gauge invariant quark Green's functions. This
allows classification of the Green's functions according to the number of
segments the polygonal lines contain. Functional relations are established
between Green's functions with polygonal lines with different numbers of
segments. An integrodifferential equation is obtained for the quark two-point
Green's function with a path along a single straight line segment where the
kernels are represented by a series of Wilson loop averages along polygonal
contours. The equation is exactly and analytically solved in the case of
two-dimensional QCD in the large-Nc​ limit. The solution displays generation
of an infinite number of dynamical quark masses accompanied with branch point
singularities that are stronger than simple poles. An approximation scheme,
based on the counting of functional derivatives of Wilson loops, is proposed
for the resolution of the equation in four dimensions.Comment: 6 pages, PDFLatex uses elsarticle class. Invited talk at the
Conference Light Cone: Relativistic Hadronic and Particle Physics, 10-15
December 2012, Delhi, Indi