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

TL;DR

This paper analytically investigates the spectral properties of a gauge invariant quark Green's function in two-dimensional QCD, revealing threshold singularities that imply quarks are not observable as free particles.

Contribution

It provides an exact integrodifferential equation solution for the Green's function and characterizes its spectral functions and singularities in two-dimensional QCD.

Findings

Spectral functions are infra-red finite and on the positive real axis.

Green's function exhibits an infinite number of threshold branch points.

Strong threshold singularities suggest quarks cannot be observed as asymptotic states.

Abstract

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-Nc limit by means of an exact integrodifferential equation. Its spectral functions are analytically determined. They are infra-red 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.