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Relativistic kinetic momentum operators, half-rapidities and noncommutative differential calculus

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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 in the Relativistic Configuration Space (RCS). 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 in the Lobachevsky momentum space (the mass shell).

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References

  1. V. G. Kadyshevsky, R. M. Mir-Kasimov, and N. B. Skachkov, “Relativistic Two-Body Problem and Expansion in Relativistic Spherical Functions,” Nuovo Cim. A 55, 233–261 (1968).

    Article  ADS  Google Scholar 

  2. R. M. Mir-Kasimov, “SUq(1,1) and Relativistic Oscillator,” J. Phys. A: Math. Gen. 24, 4283–4286 (1991).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. R. M. Mir-Kasimov, “Relation between Relativistic and Non-Relativistic Quantum Mechanics as Integral Transformation,” Found. Phys. 32, 607–631 (2002).

    Article  MathSciNet  Google Scholar 

  4. K. Koizumi, R. M. Mir-Kasimov, and I. S. Sogami, “q-Deformed and c-Deformed Harmonic Oscillators,” Prog. Theor. Phys. (Japan) 110, 819–833 (2003).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. R. M. Mir-Kasimov, “V.A. Fock’s Theory of Hydrogen Atom and Quantum Space,” Phys. Part. Nucl. 31, 44–61 (2000); Z. Can, Z. Güven, R. M. Mir-Kasimov, and O. Oguz, “Poincare Lie Algebra and Noncommutative Differential Calculus,” Phys. At. Nucl. 64, 1985–1998 (2001).

    Google Scholar 

  6. N. Ya. Vilenkin and A. U. Klimyk, Representation of Lie Groups and Special Functions (Kluwer, Dordrecht, 1991), Vols. 1–3.

    Book  MATH  Google Scholar 

  7. D. V. Woronowich, “Deformations,” Commun. Math. Phys. 122, 125 (1989); A. Connes, Non-Commutative Geometry (Academic, San Diego, 1994); A. Dimakis and F. Müller-Hoissen, J. Math. Phys. 40, 1518–1548 (1999).

    Article  ADS  Google Scholar 

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

    R. M. Mir-Kasimov

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  1. R. M. Mir-Kasimov
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Correspondence to R. M. Mir-Kasimov.

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Mir-Kasimov, R.M. Relativistic kinetic momentum operators, half-rapidities and noncommutative differential calculus. Phys. Part. Nuclei 43, 673–675 (2012). https://doi.org/10.1134/S1063779612050280

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