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Coherent State Induced Star-Product on $R^3_{\lambda}$ and the Fuzzy Sphere
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abstract
Using the Hopf fibration and starting from a four dimensional noncommutative Moyal plane, $R^2_{\theta}\times R^2_{\theta}$, we obtain a star-product for the noncommutative (fuzzy) $R^3_{\lambda}$ defined by $[x^i,x^j]=i\lambda\epsilon_{ijk}x^k$. Furthermore, we show that there is a projection function which allows us to reduce the functions on $R^3_{\lambda}$ 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 fuzzy sphere and $\rrlam$ from the corresponding field theories on $R_{theta}\times R_{\theta}$ space.
Forward citations
Cited by 3 Pith papers
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Quantization of Algebraic Varieties Defined by Casimir Polynomials via Matrix Regularization: Fuzzy $S^7$ and Beyond
A weak matrix regularization of any single-Casimir level set of a compact semisimple Lie algebra is built from reducible representations whose coadjoint orbits densely fill the variety, with fuzzy S^7 worked out explicitly.
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Charged Particle in Lie-Poisson Electrodynamics
Charged-particle mechanics in Lie-Poisson electrodynamics is formulated with explicit gauge-invariant coordinates and action, and exact solutions are worked out for the λ-Minkowski and other cases.
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Noncommutative Gauge Theories and Gravity
The paper reviews gauge-theoretic formulations of gravity in ordinary and noncommutative spaces based on the authors' earlier works.
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