In Search of Alternatives to Higgs Fields

Field equations of S² sigma model ("the A3 model") with spontaneously broken Z(2) symmetry are presented for (D + 1)-dimensional space-time. The A3 model is an extension of the sine-Gordon equation (SGE) and supports kink-like U(1) charged solitons which are generalization of neutral solitons of the SGE. Natural question arises: is the A3 model completely integrable in (1+1)-dimensional space-time? The Lorentz-invariant scalar A3 field can be viewed as promising alternative to Higgs field.