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Conference Papers Year : 2014

Two-point gauge invariant quark Green's functions with polygonal phase factor lines

H. Sazdjian

Abstract

Polygonal lines are used for the paths of the gluon field phase factors entering in the definition of gauge invariant quark Green's functions. This allows classification of the Green's functions according to the number of segments the polygonal lines contain. Functional relations are established between Green's functions with polygonal lines with different numbers of segments. An integrodifferential equation is obtained for the quark two-point Green's function with a path along a single straight line segment where the kernels are represented by a series of Wilson loop averages along polygonal contours. The equation is exactly and analytically solved in the case of two-dimensional QCD in the large-$N_c$ limit. The solution displays generation of an infinite number of dynamical quark masses accompanied with branch point singularities that are stronger than simple poles. An approximation scheme, based on the counting of functional derivatives of Wilson loops, is proposed for the resolution of the equation in four dimensions.

Dates and versions

in2p3-00877312 , version 1 (28-10-2013)

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Cite

H. Sazdjian. Two-point gauge invariant quark Green's functions with polygonal phase factor lines. International Conference on Light-Cone Physics: Hadronic and Particle Physics, Dec 2012, Delhi, India. ⟨10.1016/j.nuclphysbps.2014.04.014⟩. ⟨in2p3-00877312⟩
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