Abstract
We present an elementary non-perturbative method for obtaining Green's functions (GFs) for timelike momenta. We assume that there are no singularities in the second and fourth quadrants of the complex plane of space momentum components and perform a 3D analog of Wick rotation. This procedure defines Green's 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 wavefunction has been spontaneously generated even below the standard perturbative threshold. Therefore, our method favors a confinement mechanism based on the lack of real poles.
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