Hamiltonian analysis of gauged CP^1 model, with or without Hopf term, and fractional spin

Details Hamiltonian analysis of gauged CP^1 model, with or without Hopf term, and fractional spin Hamiltonian analysis of gauged CP^1 model, with or without Hopf term, and fractional spin

1997-10-28

arxiv.org/abs/hep-th/9710211v1

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, Latex

Scientific paper

Recently it has been shown by Cho and Kimm that the gauged $CP^1$ model, obtained by gauging the global SU(2) group of $CP^1$ model and adding a corresponding Chern-Simons term, has got its own soliton. These solitons are somewhat distinct from those of pure $CP^1$ model, as they cannot always be characterised by $\pi_2(CP^1)=Z$. In this paper, we first carry out the Hamiltonian analysis of this gauged $CP^1$ model. Then we couple the Hopf term, associated to these solitons and again carry out its Hamiltonian analysis. The symplectic structures, along with the structures of the constraints, of these two models (with or without Hopf term) are found to be essentially the same. The model with Hopf term, is then shown to have fractional spin, which however depends not only on the soliton number $N$ but also on the nonabelian charge.

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