A Gauge and Lorentz covariant approximation for the quark propagator in anarbitrary gluon field

We decompose the quark propagator in the presence of an arbitrary gluon fie ld with respect to a set of Dirac matrices. The four-dimensional integrals which arise in first order perturbation theory are rewritten as line-integr als along certain field lines, together with a weighted integration over th e various field lines. It is then easy to transform the propagator into a f orm involving path ordered exponentials. The resulting expression is non-pe rturbative and has the correct behavior under Lorentz transformations, gaug e transformations and charge conjugation. Furthermore it coincides with the exact propagator in first order of the coupling g. No expansion with respe ct to the inverse quark mass is involved, the expression can even be used f or vanishing mass. For large mass the field lines concentrate near the stra ight line connection and simple results can be obtained immediately.