On the spin of Solitons in 2+1 dimensional models

It is believed that the charged vortex in the Chern-Simons-Higgs model can have fractional spin, since the extra angular momentum of the static vortex calculated from the classical energy-momentum tensor is nonzero. We re-examine the spin of the charged vortex by use of quantum mechanical method, by which the baby skyrmion in theO(3) nonlinear -model with the Hopf term is pointed out to have fractional spin. It is shown that the spin of the charged vortex obtained from the quantum mechanical argument does not necessarily coincide with the value of classical extra angular momentum. Moreover, it is found that its value is not unique, since it is one of quantities which depend on the gauge condition of the Chern-Simons gauge field.