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On the example of a real scalar field, an approach to quantization ofnon-linear fields and construction of the perturbation theory with account ofspontaneous symmetry breaking is proposed. The method is based on using as themain approximation of the relativistic self-consistent field model, in whichthe influence of vacuum field fluctuations is taken into account whenconstructing the one-particle states. The solutions of the self-consistentequations determine possible states, which also include the states with brokensymmetries. Different states of the field are matched to particles, whosemasses are determined by both parameters of the Lagrangian and vacuumfluctuations. The density of the vacuum energy in these states is calculated.It is shown that the concept of Bogolubov's quasi-averages can naturally beapplied for definition of exact Green functions in the states with brokensymmetries. Equations for exact one- and two-point Green functions areobtained.

On the theory of a non-linear neutral scalar field with spontaneously broken symmetry