A noncommutative uniton theory. (English) Zbl 1187.58021

Summary: Harmonic two-spheres in the unitary group may be constructed and described in terms of unitons. We present an analogue of this theory for those solutions of the noncommutative \(U(1)\) sigma-model that may be represented as finite-dimensional perturbations of zero-energy solutions. In particular, we establish that the energy of every such solution is an integer multiple of \(8\pi\), describe all solutions of small energy and give many explicit examples of non-Grassmannian solutions.


58E20 Harmonic maps, etc.
53C35 Differential geometry of symmetric spaces