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Title: Relativistic differential-difference momentum operators and noncommutative differential calculus

The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics (QM) in the Relativistic Configuration Space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated as the independent term of the total Hamiltonian. This relativistic kinetic energy term is not distinguishing in form from its nonrelativistic counterpart. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generating function for the matrix elements of the unitary irreps of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS.
Authors:
 [1]
  1. Joint Institute for Nuclear Research (Russian Federation)
Publication Date:
OSTI Identifier:
22212656
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Atomic Nuclei; Journal Volume: 76; Journal Issue: 9; Other Information: Copyright (c) 2013 Pleiades Publishing, Ltd.; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; COMMUTATION RELATIONS; DIFFERENTIAL CALCULUS; EUCLIDEAN SPACE; HAMILTONIANS; KINETIC ENERGY; LORENTZ GROUPS; MATRIX ELEMENTS; POLYNOMIALS; QUANTUM MECHANICS; RELATIVISTIC RANGE; WAVE FUNCTIONS; WAVE PROPAGATION