The quantum 2sphere as a complex quantum manifold

Authors: ChongSun Chu PeiMing Ho Bruno Zumino

Publish Date: 2014/03/31

Volume: 70, Issue: 2, Pages: 339-344

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Abstract

We describe the quantum sphere of Podles for c = 0 by means of a stereographic projection which is analogous to that which exibits the classical sphere as a complex manifold We show that the algebra of functions and the differential calculus on the sphere are covariant under the coaction of fractional transformations with SU q2 coefficients as well as under the action of SU q2 vector fields Going to the classical limit we obtain the Poisson sphere Finally we study the invariant integration of functions on the sphere and find its relation with the translationally invariant integration on the complex quantum planeThis work was supported in part by the Director Office of Energy Research Office of High Energy and Nuclear Physics Division of High Energy Physics of the US Department of Energy under Contract DEAC0376SF00098 and in part by the National Science Foundation under grant PHY9021139

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