Dirac Operators for Matrix Algebras Converging to Coadjoint Orbits

Abstract In the high-energy physics literature one finds statements such as “matrix algebras converge to sphere”. Earlier I provided a general precise setting for understanding statements, in which matrix are viewed quantum metric spaces, and convergence is with respect Gromov–Hausdorff-type distance. But physicists want even more treat structures on spheres (and other spaces), vector bundles, Yang–Mills functionals, Dirac operators, etc., they approximate these by corresponding algebras. present paper we provide somewhat unified construction of operators coadjoint orbits that them. This enables us prove our main theorem, whose content that, metric-space determined construct, do indeed orbits, quite strong version Gromov–Hausdorff