Class of scalar-field soliton solutions in three space dimensions

A class of three-space-dimensional soliton solutions is given; these solitons are made of scalar fields and are of a nontopological nature. The necessary conditions for having such soliton solutions are (i) the conservation of an additive quantum number, say Q, and (ii) the presence of a neutral ($Q=0$) scalar field. It is shown that there exist two critical values of the additive quantum number, QC and QS, with QC smaller than QS. Soliton solutions exist for Q>QC. When Q>QS, the lowest soliton mass is <Qm, where m is the mass of the free charged meson field; therefore, there are solitons that are stable quantum mechanically as well as classically. When Q is between QC and QS, the soliton mass is >Qm; nevertheless, the lowest-energy soliton solution can be shown to be always classically stable, though quantum-mechanically metastable. The canonical quantization procedures are carried out. General theorems on stability are established, and specific numerical results of the solition solutions are given.