A Gauge and Lorentz covariant approximation for the quark propagator in an arbitrary gluon field |
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Authors: | D Gromes |
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Affiliation: | Institut für Theoretische Physik der Universit?t Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany, DE
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Abstract: | We decompose the quark propagator in the presence of an arbitrary gluon field with respect to a set of Dirac matrices. The
four-dimensional integrals which arise in first order perturbation theory are rewritten as line-integrals along certain field
lines, together with a weighted integration over the various field lines. It is then easy to transform the propagator into
a form involving path ordered exponentials. The resulting expression is non-perturbative and has the correct behavior under
Lorentz transformations, gauge transformations and charge conjugation. Furthermore it coincides with the exact propagator
in first order of the coupling g. No expansion with respect to the inverse quark mass is involved, the expression can even be used for vanishing mass. For
large mass the field lines concentrate near the straight line connection and simple results can be obtained immediately.
Received: 31 March 2001 / Revised version: 3 May 2001 / Published online: 8 June 2001 |
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