Chapter II. Stability of Chiral Solitons

Abstract

We review studies on the stability of various chiral solitons both in the classical and quantum levels with and without the Skyrme term as the stabilizer. The effects of the couplings with the vector mesons on the stability of the chiral solitons are also discussed. The quantization of solitons is implemented in terms of the collective coordinate method and we consider here the spin-isospin rotations and the breathing motion of the solitons. It is shown that the chiral solitons are dynamically stable when the Lagrangian contains the stabilizer term. with higher derivatives and/ or the coupling with the w meson is introduced. In the case of the chiral soliton coupled with the p mesons, either the parity conserving or the spontaneously pe].rity violating occur depending on the parame­ ters of the Lagrangian. When the stabilizer is absent, the soliton coupled with the p meson decays through the parity violating states, even the effects of quantization of rotational and breathing modes are taken into account. When the stabilizer effect is weak, there appear the frozen states where the quantum motions of the spin-isospin rotational. modes and the breathing mode are completely pressed down.