Large order calculations in gauge theories

The perturbation series asymptotics are estimated by the coupling constant dispersion relations in the Yang-Mills theory. It is found that the Green functions in this theory have the imaginary parts at physical values of the coupling constant which are connected with the tunneling to the other vacuum states. These imaginary parts are calculated by the steepest descent method. The saddle points are shown to be the instanton-antiinstanton configurations of the fields. (Auth.)