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Composite system in deformed space with minimal length

par Quesne, Christiane ;Tkachuk, Volodymyr
Référence Physical review. A, Atomic, Molecular, and Optical Physics, 81, 1, 012106
Publication Publié, 2010

Article révisé par les pairs

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Résumé :

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 3.3×10-18 m. 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 2.4×10-17 m is deduced, which appears close to that obtained for electrons. © 2010 The American Physical Society.