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

Journal Article · Fri Feb 15 04:00:00 EST 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.77.045028· OSTI ID:21039192

Sazdjian, H ^[1]

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1. IPN, Universite Paris-Sud 11, CNRS/IN2P3, F-91405 Orsay (France)

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.

• OSTI ID: 21039192
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 77; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
GAUGE INVARIANCE
GLUONS
GREEN FUNCTION
INTEGRAL EQUATIONS
KERNELS
QUANTUM CHROMODYNAMICS
QUARK-ANTIQUARK INTERACTIONS
RESOLUTION
WILSON LOOP