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, Q₂ and Qₒ, with Q₂ smaller than Qₒ. Soliton solutions exist for Q>Q₂. When Q>Qₒ, the lowest 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.