Composite system in deformed space with minimal length

C. Quesne and V. M. Tkachuk
Phys. Rev. A 81, 012106 – Published 12 January 2010

Abstract

For composite systems made of N different particles living in a space characterized by the same deformed Heisenberg algebra, but with different deformation parameters, we define the total momentum and the center-of-mass position to first order in the deformation parameters. Such operators satisfy the deformed algebra with effective deformation parameters. As a consequence, a two-particle system can be reduced to a one-particle problem for the internal motion. As an example, the correction to the hydrogen atom nS energy levels is re-evaluated. Comparison with high-precision experimental data leads to an upper bound of the minimal length for the electron equal to 3.3×1018m. The effective Hamiltonian describing the center-of-mass motion of a macroscopic body in an external potential is also found. For such a motion, the effective deformation parameter is substantially reduced due to a factor 1/N2. This explains the strangely small result previously obtained for the minimal length from a comparison with the observed precession of the perihelion of Mercury. From our study, an upper bound of the minimal length for quarks equal to 2.4×1017m is deduced, which appears close to that obtained for electrons.

  • Received 28 May 2009

DOI:https://doi.org/10.1103/PhysRevA.81.012106

©2010 American Physical Society

Authors & Affiliations

C. Quesne1,* and V. M. Tkachuk2,†

  • 1Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels, Belgium
  • 2Department of Theoretical Physics, Ivan Franko National University of Lviv, 12 Drahomanov St., Lviv, UA-79005, Ukraine

  • *cquesne@ulb.ac.be
  • tkachuk@ktf.franko.lviv.ua

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Issue

Vol. 81, Iss. 1 — January 2010

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