A model for Hopfions on the space-time S^3 x R
Abstract
We construct static and time dependent exact soliton solutions for a theory of scalar fields taking values on a wide class of two dimensional target spaces, and defined on the four dimensional space-time S^3 x R. The construction is based on an ansatz built out of special coordinates on S^3. The requirement for finite energy introduces boundary conditions that determine an infinite discrete spectrum of frequencies for the oscillating solutions. For the case where the target space is the sphere S^2, we obtain static soliton solutions with non-trivial Hopf topological charges. In addition, such hopfions can oscillate in time, preserving their topological Hopf charge, with any of the frequencies belonging to that infinite discrete spectrum.
Keywords
Cite
@article{arxiv.hep-th/0406244,
title = {A model for Hopfions on the space-time S^3 x R},
author = {E. De Carli and L. A. Ferreira},
journal= {arXiv preprint arXiv:hep-th/0406244},
year = {2009}
}
Comments
Enlarged version with the time-dependent solutions explicitly given. One reference and two eps figures added. 14 pages, latex