Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers

Details Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers

1999-05-11

arxiv.org/abs/hep-th/9905079v1

Phys.Rev.Lett. 83 (1999) 1723-1726

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 7 pgs

Scientific paper

10.1103/PhysRevLett.83.1723

In this paper we construct explicitly an infinite number of Hopfions (static, soliton solutions with non-zero Hopf topological charges) within the recently proposed 3+1-dimensional, integrable and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are constructed explicitly in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

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