Gauge-invariant quark propagator in QCD

The matrix elements of the simplest quark-antiquark nonlocal gauge-invariant operators between the vacuum and a one-pion state are studied. On the basis of quark-hadron duality, the dependence of these matrix elements on the spacetime interval between the points is obtained explicitly to the leading order in interaction. The soft-pion technique makes it possible to derive an explicit formula for the gauge-invariant propagator of a light quark in an external gluon field. The proposed model is compared with other approaches.