Year: 2002
Type: article
Abstract: Using the Hopf fibration and starting from a four-dimensional noncommutative Moyal plane ${R}_{\ensuremath{\theta}}^{2}\ifmmode\times\else\texttimes\fi{}{R}_{\ensuremath{\theta}}^{2}$ we obtain a star product for the noncommutative (fuzzy) ${R}_{\ensuremath{\lambda}}^{3}$ defined by $[{x}^{i}{,x}^{j}]=i\ensuremath{\lambda}{\ensuremath{\epsilon}}_{\mathrm{ijk}}{x}^{k}.$ Furthermore, we show that there is a projection function which allows us to reduce the functions on ${R}_{\ensuremath{\lambda}}^{3}$ to that of the fuzzy sphere, and hence we introduce a new star product on the fuzzy sphere. We will then briefly discuss how using our method one can extract information about the field theory on the fuzzy sphere and ${R}_{\ensuremath{\lambda}}^{3}$ from the corresponding field theories on ${R}_{\ensuremath{\theta}}^{2}\ifmmode\times\else\texttimes\fi{}{R}_{\ensuremath{\theta}}^{2}$ space.
Authors: A. B. Hammou, M. Lagraa, M. M. Sheikh-Jabbari
Language: Latvian
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1762895007