Gauge-invariant approach to quark dynamics

Abstract

The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of quantum chromodynamics (QCD) are first reviewed. The role of the parallelm transport operation in constructing gauge-invariant Green’s functions is then 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 presented. An integro-differential equation, obtained for the quark Green’s function defined with a phase factor along a single, straight line segment, 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.

Keywords

QCD / quarks / gluons / parallel transport / Wilson loops / gauge-invariant Green’s functions

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Funding

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg