  We present an elementary nonperturbative method to obtain Green's functions
(GFs) for timelike momenta. We assume there are no singularities in the first
and third quadrants of the complex plane of space momentum components and
perform a 3d analogue of Wick rotation. This procedure defines Greens functions
in a timelike Euclidean space. As an example we consider the quark propagator
in QCD. While for weak coupling, this method is obviously equivalent to
perturbation theory, for a realistic QCD coupling a complex part of the quark
mass and renormalization wave function has been spontaneously generated even
below the standard perturbative threshold. Therefore, our method favors a
confinement mechanism based on the lack of real poles.
