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Differential calculus on quantum spheres

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Abstract

Three-dimensional differential calculus on quantum spheres S sup2infμc ,μ∈]−1, 1[∖{0}, c∈[0, ∞], is introduced and investigated. Spectra of generalized Laplacians are found. These operators are expressed by generalized directional derivatives. Classical limits of these objects are obtained and a simple approach to quantum mechanics on a quantum sphere is presented.

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References

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Authors and Affiliations

  1. Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Hoża 74, PL 00-682, Warsaw, Poland

    Piotr Podleś

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  1. Piotr Podleś
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Podleś, P. Differential calculus on quantum spheres. Lett Math Phys 18, 107–119 (1989). https://doi.org/10.1007/BF00401865

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  • DOI: https://doi.org/10.1007/BF00401865

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