On the Classification of the Lévy-Leblond Spinors

Abstract

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 differential operators depending on the time and space coordinates.

8 pages; based on the L. M.'s talk at ISQS28, Prague, July 1-5, 2024; to appear in the Proceedings

References in corpus (2)

• Lie algebraic Carroll/Galilei duality
• Graded colour Lie superalgebras for solving Lévy-Leblond equations