Simple toy model is used in order to exhibit the technique of extracting the
non-perturbative information about Green's functions in Minkowski space. The
effective charge and the dynamical electron mass are calculated in strong
coupling 3+1 QED by solving the coupled Dyson-Schwinger equations for electron
and photon propagators. The minimal Ball-Chiu vertex was used for simplicity
and we impose the Landau gauge fixing on QED action. The solution obtained
separately in Euclidean and Minkowski space were compared, the latter one was
extracted with the help of spectral technique.Comment: 23 pages, 4 figures, v4: revised and extended version, one
introductory section adde
