Phase Structure of a Quantized Chiral Soliton on S^3 : Particles and Fields

概要

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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 hedgehog ansatz. We determine eigenenergies of the quantized S^3 skyrmion by solving the Schrodinger 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 are either symmetric or anti-symmetric under the 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 degenerate completely. When the S^3 radius is 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→∞.
理論物理学刊行会の論文
1993-11-25