Gauge-invariant approach to quark dynamics

TL;DR

This paper reviews a gauge-invariant method for describing quark dynamics in nonperturbative QCD, emphasizing Wilson loops and parallel transport, and presents an exact solution in 2D QCD showing dynamical mass generation.

Contribution

It introduces a new approach using polygonal lines for parallel transport and provides an exact analytical solution in two-dimensional QCD.

Findings

Exact solution in 2D QCD with large N_c limit

Demonstration of dynamical mass generation for quarks

Identification of strong branch-cut singularities

Abstract

The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of QCD are first reviewed. In particular, the role of the parallel transport operation in constructing gauge-invariant Green's functions is presented, and the relevance of Wilson loops for the representation of the interaction is emphasized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are then presented. An integro-differential equation is obtained for the quark Green's function defined with a phase factor along a single, straight line segment. It is solved exactly and analytically in the case of two-dimensional QCD in the large $N_c$ limit. The solution displays the dynamical mass generation phenomenon for quarks, with an infinite number of branch-cut singularities that are stronger than simple poles.