Integral equation for gauge invariant quark two-point Green's function in QCD

Abstract

Gauge invariant quark two-point Green's functions defined with path-ordered gluon field phase factors along skew-polygonal lines joining the quark to the antiquark are considered. Functional relations between Green's functions with different numbers of path segments are established. An integral equation is obtained for the Green's function defined with a phase factor along a single straight line. The equation implicates an infinite series of two-point Green's functions, having an increasing number of path segments; the related kernels involve Wilson loops with contours corresponding to the skew-polygonal lines of the accompanying Green's function and with functional derivatives along the sides of the contours. The series can be viewed as an expansion in terms of the global number of the functional derivatives of the Wilson loops. The lowest-order kernel, which involves a Wilson loop with two functional derivatives, provides the framework for an approximate resolution of the equation.

28 pages, 4 figures

References in corpus (4)

• A consistent derivation of the quark--antiquark and three quark potentials in a Wilson loop context
• The Feynman-Schwinger representation in QCD
• Bound state equation in the Wilson loop approach with minimal surfaces
• Bethe--Salpeter equation in QCD

Cited by in corpus (6)

• Spectral properties of the gauge invariant quark Green's function in two-dimensional QCD
• Gauge invariant bound state equations for quark-antiquark systems in QCD
• Properties of the gauge invariant quark Green's function in two-dimensional QCD
• Gauge-invariant approach to quark dynamics
• On the role of dynamical quark mass generation in chiral symmetry breaking in QCD
• Two-point gauge invariant quark Green's functions with polygonal phase factor lines