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Foldy–Wouthuysen Transformation of Noncommutative Dirac Equation in the Presence of Minimal Uncertainty in Momentum

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Abstract

In this paper, by using the canonical Foldy–Wouthuysen transformation for relativistic spin-1/2 particles, we investigate the non-relativistic limit and determine the basic properties of the Dirac equation in the presence of a minimal uncertainty in momentum within a noncommutative phase-space. This leads to obtaining a deformed Schrödinger– Pauli equation; there, we examine the effect of both the noncommutativity in phase-space and the minimal uncertainty in momentum on the non-relativistic limit of the Dirac equation. However, with both Bopp– Shift linear transformation, and the Moyal– Weyl product (\(\star \)product), we introduce the noncommutativity in phase-space. We as well test the efficacy and behavior of the Foldy– Wouthuysen transformation in deriving the non-relativistic limit under certain conditions and influences.

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  1. Laboratoire de Physique Mathématique et de Physique Subatomique (LPMPS), Université Frères Mentouri, 25000, Constantine, Algeria

    Ilyas Haouam

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Haouam, I. Foldy–Wouthuysen Transformation of Noncommutative Dirac Equation in the Presence of Minimal Uncertainty in Momentum. Few-Body Syst 64, 9 (2023). https://doi.org/10.1007/s00601-023-01790-4

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