On the Classification of the Lévy-Leblond Spinors

• URL: http://arxiv.org/abs/2411.14139v1
• Date: Thu, 21 Nov 2024 14:02:27 GMT
• Title: On the Classification of the Lévy-Leblond Spinors
• Authors: Luiza Miranda, Isaque P. de Freitas, Francesco Toppan,
• Abstract summary: First-order L'evy-Leblond differential equations are non-relativistic analogous to the Dirac equation. We show how to extend to the L'evy-Leblond spinors the real/complex/quaternionic classification of the relativistic spinors.
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• Abstract: The first-order L\'evy-Leblond differential equations (LLEs) are the non-relativistic analogous of the Dirac equation: they are the "square roots" of the Schr\"odinger equation in ($1+d$) dimensions and admit spinor solutions. In this paper we show how to extend to the L\'evy-Leblond spinors the real/complex/quaternionic classification of the relativistic spinors (which leads to the notions of Dirac, Weyl, Majorana, Majorana-Weyl, Quaternionic spinors). Besides the free equations, we also consider the presence of potential terms. Applied to a conformal potential, the simplest $(1+1)$-dimensional LLE induces a new differential realization of the $osp(1|2)$ superalgebra in terms of differential operators depending on the time and space coordinates.

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