Landau ghost pole problem in quantum field theory: From 50th of last century to the present day

In this paper we present our results of the investigation of asymptotical behavior of amplitude at short distances in four-dimensional scalar field theory with ϕ⁴ interaction. To formulate of our calculating model – two-particle approximation of the mean-field expansion we have used an Rochev's iteration scheme of solution of the Schwinger-Dyson equations with the fermion bilocal source. We have considered the nonlinear integral equations in deep-inelastic region of momenta. As result we have a non-trivial behavior of amplitude at large momenta.