Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-05-18
Proc.Roy.Soc.Lond.A463:945-959,2007
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, one figure. References added and boundary conditions clarified. Final version, to appear in the Proceedings of the R
Scientific paper
10.1098/rspa.2006.1799
We consider a class of time dependent finite energy multi-soliton solutions of the U(N) integrable chiral model in $(2+1)$ dimensions. The corresponding extended solutions of the associated linear problem have a pole with arbitrary multiplicity in the complex plane of the spectral parameter. Restrictions of these extended solutions to any spacelike plane in $\R^{2,1}$ have trivial monodromy and give rise to maps from a three sphere to U(N). We demonstrate that the total energy of each multi-soliton is quantised at the classical level and given by the third homotopy class of the extended solution. This is the first example of a topological mechanism explaining classical energy quantisation of moving solitons.
Dunajski Maciej
Plansangkate Prim
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