Resumo
The first-order Lévy-Leblond differential equations (LLEs) are the
non-relativistic analogous of the Dirac equation: they are the
“square roots” of the Schrödinger equation in ($1+d$) dimensions and
admit spinor solutions. In this paper we show how to extend to the Lévy-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 first-order differential operators depending on the time and space coordinates.