Physics NotePublished
On the Classification of the Lévy-Leblond Spinors
Luiza Miranda; Isaque P. de Freitas; F. Toppan
Publication details
- Authors
- Luiza Miranda; Isaque P. de Freitas; F. Toppan
- Type
- Physics Note
- Status
- Published
- Publication date
- 22/11/2024
- Description
- 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.
- Year
- 2024
- Number
- CBPF-NF-003/24
- Linked to a thesis
- No
- Linked to a grant
- No