  On the example of a real scalar field, an approach to quantization of
non-linear fields and construction of the perturbation theory with account of
spontaneous symmetry breaking is proposed. The method is based on using as the
main approximation of the relativistic self-consistent field model, in which
the influence of vacuum field fluctuations is taken into account when
constructing the one-particle states. The solutions of the self-consistent
equations determine possible states, which also include the states with broken
symmetries. Different states of the field are matched to particles, whose
masses are determined by both parameters of the Lagrangian and vacuum
fluctuations. The density of the vacuum energy in these states is calculated.
It is shown that the concept of Bogolubov's quasi-averages can naturally be
applied for definition of exact Green functions in the states with broken
symmetries. Equations for exact one- and two-point Green functions are
obtained.
