Static solitons with non-zero Hopf number

Abstract

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.

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

References in corpus (1)

• Multisolitons in a Two-dimensional Skyrme Model

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