Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2007-09-03
Phys.Rev.D77:045028,2008
Physics
High Energy Physics
High Energy Physics - Phenomenology
28 pages, 4 figures
Scientific paper
10.1103/PhysRevD.77.045028
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.
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