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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.
Friedberg et al. (Sat,) studied this question.