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Monopoles and solitons in fuzzy physics. (English) Zbl 0954.58026

Summary: Monopoles and solitons have important topological aspects like quantized fluxes, winding numbers and curved target spaces. Naive discretizations which substitute a lattice of points for the underlying manifolds are incapable of retaining these features in a precise way. We study these problems of discrete physics and matrix models and discuss mathematically coherent discretizations of monopoles and solitons using fuzzy physics and noncommutative geometry. A fuzzy \(\sigma\)-model action for the two-sphere fulfilling a fuzzy Belavin-Polyakov bound is also put forth.

MSC:

58J90 Applications of PDEs on manifolds
81R99 Groups and algebras in quantum theory
81T99 Quantum field theory; related classical field theories
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