Are Vortex Numbers Preserved?

Details Are Vortex Numbers Preserved? Are Vortex Numbers Preserved?

2006-12-14

arxiv.org/abs/math-ph/0612041v2

J.Geom.Phys.58:967-978,2008

Physics

Mathematical Physics

Typos are corrected, some references are added, 20pages, no figure

Scientific paper

10.1016/j.geomphys.2008.03.004

We study noncommutative vortex solutions that minimize the action functional of the Abelian Higgs model in 2-dimensional noncommutative Euclidean space. We first consider vortex solutions which are deformed from solutions defined on commutative Euclidean space to the noncommutative one. We construct solutions whose vortex numbers are unchanged under the noncommutative deformation. Another class of noncommutative vortex solutions via a Fock space representation is also studied.

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