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Symmetry 2019, 11(2), 223; https://doi.org/10.3390/sym11020223

The Non-Relativistic Limit of the DKP Equation in Non-Commutative Phase-Space

Laboratoire de Physique Mathématique et de Physique Subatomique (LPMPS), Université Frères Mentouri, Constantine 25000, Algeria
Received: 11 December 2018 / Revised: 23 January 2019 / Accepted: 31 January 2019 / Published: 14 February 2019
(This article belongs to the Special Issue Mathematical Physics and Symmetry)
Full-Text   |   PDF [311 KB, uploaded 27 February 2019]

Abstract

The non-relativistic limit of the relativistic DKP equation for both of zero and unity spin particles is studied through the canonical transformation known as the Foldy–Wouthuysen transformation, similar to that of the case of the Dirac equation for spin-1/2 particles. By considering only the non-commutativity in phases with a non-interacting fields case leads to the non-commutative Schrödinger equation; thereafter, considering the non-commutativity in phase and space with an external electromagnetic field thus leads to extract a phase-space non-commutative Schrödinger–Pauli equation; there, we examined the effect of the non-commutativity in phase-space on the non-relativistic limit of the DKP equation. However, with both Bopp–Shift linear transformation through the Heisenberg-like commutation relations, and the Moyal–Weyl product, we introduced the non-commutativity in phase and space. View Full-Text
Keywords: DKP equation; noncommutative DKP equation; Schrödinger equation; noncommutative SchrödingerPauli equation; phase-space noncommutativity; Foldy-Wouthuysen transformation; non-relativistic limit DKP equation; noncommutative DKP equation; Schrödinger equation; noncommutative SchrödingerPauli equation; phase-space noncommutativity; Foldy-Wouthuysen transformation; non-relativistic limit
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Haouam, I. The Non-Relativistic Limit of the DKP Equation in Non-Commutative Phase-Space. Symmetry 2019, 11, 223.

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