Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-06-09
J.Phys.A43:205203,2010
Physics
High Energy Physics
High Energy Physics - Theory
9 pages, 3 Figures, Minor changes in the abstract have been made. The manuscript has been modified for better clarity. A refer
Scientific paper
10.1088/1751-8113/43/20/205203
We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in $\mathbb{R}^3$. We find that several surfaces, differing by constants, are described by the Higgs algebra at the fuzzy level. Some of these surfaces have a singularity and we overcome this by quantizing this manifold using coherent states for this nonlinear algebra. This is seen in the measure constructed from these coherent states. We also find the star product for this non-commutative algebra as a first step in constructing field theories on such fuzzy spaces.
Govindarajan T. R.
Padmanabhan Pramod
Shreecharan T.
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