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

Journal Article · Mon Nov 15 00:00:00 EST 2010 · Physics of Particles and Nuclei

DOI:https://doi.org/10.1134/S1063779610060328· OSTI ID:22974996

Mir-Kasimov, R. M. ^[1]

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

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.

• OSTI ID: 22974996
• Journal Information: Physics of Particles and Nuclei, Vol. 41, Issue 6; Other Information: Copyright (c) 2010 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7796
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMMUTATION RELATIONS
DIFFERENTIAL CALCULUS
EIGENFUNCTIONS
EUCLIDEAN SPACE
LORENTZ GROUPS
MATRICES
MATRIX ELEMENTS
POLYNOMIALS
QUANTUM MECHANICS