Spectral properties of the gauge invariant quark Green's function in two-dimensional QCD

The gauge invariant quark Green’s function with a path-ordered phase factor along a straight line is studied in two-dimensional QCD in the large-N_c limit by means of an exact integrodifferential equation. Its spectral functions are analytically determined. They are infrared finite and lie on the positive real axis of the complex plane of the momentum squared variable, corresponding to momenta in the forward light cone. Their singularities are represented by an infinite number of threshold type branch points with power-law -3/2, starting at positive mass values, characterized by an integer number n and increasing with n. The analytic expression of the Green’s function for all momenta is presented. The appearance of strong threshold singularities is suggestive of the fact that quarks could not be observed as asymptotic states.