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

TL;DR

This paper analytically studies the gauge invariant quark Green's function in two-dimensional QCD, revealing its infrared finiteness and complex singularity structure with an exact solution.

Contribution

It provides an exact integrodifferential equation solution for the gauge invariant quark Green's function in 2D QCD at large N_c, detailing its singularities and finiteness.

Findings

Green's function is infrared finite

Singularities are infinite threshold branch points

Solution is analytically determined

Abstract

Using an exact integrodifferential equation we study the properties of the gauge invariant quark Green's function, defined with a path-ordered gluon field phase factor along a straight line, in two-dimensional QCD in the large-N_c limit. The Green's function is found to be infrared finite with singularities represented by an infinite number of threshold type branch points with a power equal to -3/2, starting at positive mass squared values. The solution is analytically determined.