Noncommutative Geometry¶and Gauge Theory on Fuzzy Sphere

1998/01/31 by Ursula Carow-Watamura, Satoshi Watamura · 6 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebra over a field #Algebraic and Geometric Analysis #Bimodule #Fuzzy logic #Fuzzy sphere #Gauge theory #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Quantum differential calculus #Supersymmetric gauge theory #hep-th

paper · pdf · doi:10.1007/s002200000213

published as Commun.Math.Phys. 212 (2000) 395-413 · LaTeX 26 pages, final version (Dec.1999) accepted in CMP. An extra term in the gauge action is discussed

arxiv created 2000/03/23 · openalex publication_date 2000/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

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