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arXiv · 2411.14139

On the Classification of the L\'evy-Leblond Spinors

Luiza Miranda·Isaque P. de Freitas·Francesco Toppan
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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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Luiza Miranda, Isaque P. de Freitas, Francesco Toppan. 2024-11-21. On the Classification of the L\'evy-Leblond Spinors. https://doi.org/10.1088/1742-6596%2F2912%2F1%2F012034

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