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Generating function for extended Jacobi polynomials, noncommutative differential calculus and the relativistic energy and momentum operators

  • Session “Quantum Field Theory and Theory of Elementary Particles”
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Abstract

It is shown that the generating function for the matrix elements of irreps of Lorentz group is the common eigenfunction of the interior derivatives of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions. These derivatives commute and can be interpreted as the quantum mechanical operators of the relativistic momentum corresponding to the half of the non-Euclidean distance from the origin in the Lobachevsky momentum space.

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Russia Namik Kemal University, Tekirdag, Turkey

    R. M. Mir-Kasimov

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  1. R. M. Mir-Kasimov
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Mir-Kasimov, R.M. Generating function for extended Jacobi polynomials, noncommutative differential calculus and the relativistic energy and momentum operators. Phys. Part. Nuclei 41, 969–972 (2010). https://doi.org/10.1134/S1063779610060328

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  • DOI: https://doi.org/10.1134/S1063779610060328

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