Class of scalar-field soliton solutions in three space dimensions

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, ${Q}_{C}$ and ${Q}_{S}$, with ${Q}_{C}$ smaller than ${Q}_{S}$. Soliton solutions exist for $Q>{Q}_{C}$. When $Q>{Q}_{S}$, the lowest soliton mass is $<\mathrm{Qm}$, 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 ${Q}_{C}$ and ${Q}_{S}$, the soliton mass is $>\mathrm{Qm}$; 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.