Class of scalar-field soliton solutions in three space dimensions

TLDR: A class of three-space-dimensional soliton solutions is given in this paper, which are made of scalar fields and are of a nontopological nature; the necessary conditions for having such soliton solution are (I) the conservation of an additive quantum number, say Q, and (II) the presence of a neutral (Q = 0) scalar field.

Abstract: 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, Q/sub C/ and Q/sub S/, with Q/sub C/ smaller than Q/sub S/. Soliton solutions exist for Q > Q/sub C/. When Q > Q/sub S/, the lowest soliton mass is Qm; never and Q/sub S/, 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 soliton solutions are given. (AIP)