Phase Structure of a Quantized Chiral Soliton on S3

A quantization of a breathing motion of a rotating chiral soliton on $S^3$ isperformed in terms of a family of trial functions for a profile function of thehegdehog ansatz. We determine eigenenergies of the quantized $S^3$ skyrmion bysolving the Schr\"odinger equation of the breathing mode for several lower spinand isospin states varying the Skyrme term constants $e$. When $S^3$ radius issmaller than $2/ef_\pi$, where $f_\pi$ is the pion decay constant, we alwaysobtain a conformal map solution as the lowest eigenenergy state. In theconformal map case, allowed states have only symmetric or anti-symmetric wavefunction under inversion of a dynamical variable describing the breathing mode.As the $S^3$ radius increases the energy splitting between the symmetric andanti-symmetric states rapidly decreases and two states become completelydegenerate state. When the $S^3$ radius larger than $3/ef_\pi$, for the smallSkyrme term constant $e$ the lowest eigenenergy states are obtained with theprofile function given by an arccosine form which is almost the same to thoseof 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 ofconformal map, which correspond to the \lc\lc frozen states" for the $R^3$skyrmion as the limit of $S^3$ radius $ \to \infty$.Comment: 23 pages, plain TEX, 11 figures (not included, upon request