Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 158

Solutions of a 2-dimensional Skyrme-Model on Aff(R)

A. Schmitt

No explicit solutions of the Skyrme field equation have been found since its formulation, more than 33 years ago. Here we reduce this equation to a 2-dimensional model, for which we obtain a whole class of solutions. Therefore, we change the 3-dimensional SU(2)-valued field to a 2-dimensional Aff(R)-valued field, where Aff(R) is the only 2-dimensional, connected, non commutative Lie group. We will give examples for this reduced field equation.

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