Noncommutative Geometry and Gauge Theory on Fuzzy Sphere

Abstract

The differential algebra on the fuzzy sphere is constructed by applying Connes' scheme. The U(1) gauge theory on the fuzzy sphere based on this differential algebra is defined. The local U(1) gauge transformation on the fuzzy sphere is identified with the left $U(N+1)$ transformation of the field, where a field is a bimodule over the quantized algebra \CA_N. The interaction with a complex scalar field is also given.Comment: LaTeX 26 pages, final version (Dec.1999) accepted in CMP. An extra term in the gauge action is discusse