Spontaneous symmetry breaking in the interaction of a scalar field with an external vector field

A model is constructed of the spontaneous breaking of gauge invariance in the interaction of a scalar field with a nonstationary vector field of special form. In contrast to the models of Goldstone and Higgs, the unrenormalized mass is assumed to be real. It is shown that an external field of definite frequency can lead to spontaneous symmetry breaking in the originally symmetric system.