Regensburg 1998 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 7: Strukturelle Fragen der Quantenfeldtheorie

MP 7.1: Fachvortrag

Thursday, March 26, 1998, 14:00–14:20, H45

Differential Calculus on the "Fuzzy Supersphere" — •G. Reiter¹ and H. Grosse² — ¹Institut für Theoretische Physik, Technische Universität Graz, Petersgasse 16, A-8010 Graz — ²Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090 Wien

Starting with the Z₂-graded algebra of H^∞-functions on the (2,2)-dimensional supersphere and the natural action of the orthosymplectic Lie superalgebra osp(1,2) on this algebra we introduce the "Fuzzy Supersphere" in close analogy to the "Fuzzy Sphere". Moreover a noncommutative pendant to the super-de Rham complex an the (2,2)-dimensional supersphere is developed. The isomorphism of the super-de Rham cohomology of the (2,2)-dimensional supersphere and the de Rham cohomology of its body (2-sphere) is reproduced on the "fuzzy level".