Using gauge invariant quark Green's functions, defined with path-ordered gluon field phase factors along polygonal lines, and functional relations among them, two compatible bound state equations of the Dirac type are established for quark-antiquark systems, each relative to the quark or to the antiquark of the system. The kernels of the bound state equations are defined through series of Wilson loop averages along closed polygonal contours and their functional derivatives on them. A sufficient criterion for spontaneous chiral symmetry breaking is derived, relating the Goldstone boson wave function in the zero total momentum limit with the scalar part of the gauge invariant quark two-point Green's function.