Quantum solitons with cylindrical symmetry

Soliton solutions with cylindrical symmetry are investigated within the nonlinear $\sigma$-model disregarding the Skyrme-stabilization term. The solitons are stabilized by quantization of the collective breathing mode and collapse in the $\hbar \rightarrow 0$ limit. It is shown that for such stabilization mechanism the model, apart from the solitons with integer topological number ${\mathbf B}$, admits the solitons with half-odd ${\mathbf B}$. The solitons with integer ${\mathbf B}$ have standard spin-isospin classification, but the ${\mathbf B}={\displaystyle {1\over 2}}$ solitons are shown to be characterized by spin, isospin and some additional “momentum”.