  Classical and quantum complex nonlinear scalar fields are considered. A new
approach to the quantization of nonlinear fields and the construction of a
perturbation theory with allowance for spontaneous symmetry breaking is
proposed, based on the use of the relativistic model of a self-consistent field
as the main approximation. The concept of a particle is analyzed within the
frame-work of the theory of nonlinear quantum fields. When constructing
single-particle states, the contribution of vacuum fluctuations is
systematically taken into account. Within the framework of the developed
approach, the problem of the existence of massless scalar particles is
discussed. It is shown that successive consideration of the vacuum averages of
not only one field operator, but also the products of two field operators,
leads to the appearance of masses for scalar particles. Various states in which
the field can exist for given parameters entering into the Lagrangian are
considered, and the vacuum energy densities in these states are calculated. It
is shown that, depending on the values of the parameters entering into the
Lagrangian, the vacuum energy density can be either positive or negative, which
is important for modern cosmology.

High Energy Physics - Theory;Quantum Physics