Phase Structure of a Quantized Chiral Soliton on S

A quantization of a breathing motion of a rotating chiral soliton on S 3 is performed in terms of a family of trial functions for a profile function of the hegdehog ansatz. We determine eigenenergies of the quantized S 3 skyrmion by solving the Schrödinger equation of the breathing mode for several lower spin and isospin states varying the Skyrme term constants e. When S 3 radius is smaller than 2/ef π , where f π is the pion decay constant, we always obtain a conformal map solution as the lowest eigenenergy state. In the conformal map case, allowed states have only symmetric or anti-symmetric wave function under inversion of a dynamical variable describing the breathing mode. As the S 3 radius increases the energy splitting between the symmetric and anti-symmetric states rapidly decreases and two states become completely degenerate state. When the S 3 radius larger than 3/ef π , for the small Skyrme term constant e the lowest eigenenergy states are obtained with the profile function given by an arccosine form which is almost the same to those of usual R 3 skyrmion. When the effects of the Skyrme term are weak, i.e. large e, the lowest energy states are obtained by the profile function of conformal map, which correspond to the " frozen states " for the R 3 skyrmion as the limit of S 3 radius → ∞.