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Classical and quantum complex nonlinear scalar fields are considered. A newapproach to the quantization of nonlinear fields and the construction of aperturbation theory with allowance for spontaneous symmetry breaking isproposed, based on the use of the relativistic model of a self-consistent fieldas the main approximation. The concept of a particle is analyzed within theframe-work of the theory of nonlinear quantum fields. When constructingsingle-particle states, the contribution of vacuum fluctuations issystematically taken into account. Within the framework of the developedapproach, the problem of the existence of massless scalar particles isdiscussed. It is shown that successive consideration of the vacuum averages ofnot only one field operator, but also the products of two field operators,leads to the appearance of masses for scalar particles. Various states in whichthe field can exist for given parameters entering into the Lagrangian areconsidered, and the vacuum energy densities in these states are calculated. Itis shown that, depending on the values of the parameters entering into theLagrangian, the vacuum energy density can be either positive or negative, whichis important for modern cosmology.

Does a massless Goldstone boson exist?