Static solitons with non-zero Hopf number

Details Static solitons with non-zero Hopf number Static solitons with non-zero Hopf number

1996-09-03

arxiv.org/abs/hep-th/9609035v2

Phys.Rev. D56 (1997) 5194-5199

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, RevTeX, 7 Postscript figures, minor changes have been made, a reference has been corrected and a figure replaced

Scientific paper

10.1103/PhysRevD.56.5194

We investigate a generalized non-linear O(3) $\sigma$-model in three space dimensions where the fields are maps $S^3 \mapsto S^2$. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model exhibits soliton solutions of closed vortex type which have a lower topological bound on their energies. We explicitly compute the fields for topological charge 1 and 2 and discuss their shapes and binding energies. The effect of an additional potential term is considered and an approximation is given for the spectrum of slowly rotating solitons.

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