Eur. Phys. J. B 3, 517-534 (1998)
https://doi.org/10.1007/s100510050342

A new construction for spinor wave equations

¹ Laboratoire de Physique de la Matière Condensée (CNRS UMR 6622) , Université de Nice-Sophia Antipolis, Parc Valrose, B.P. 71, 06108 Nice Cedex , France
² Service de Physique de l'État Condensé, Centre d'Études de Saclay, l'Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France

Corresponding authors: ^a sdetoro@spec.saclay.cea.fr - ^b vanneste@ondine.unice.fr

Received: 3 November 1997
Revised: 9 February 1998
Accepted: 16 February 1998
Published online: 15 June 1998

Abstract

The construction of discrete scalar wave propagation equations in arbitrary inhomogeneous media was recently achieved by using elementary dynamical processes realizing a discrete counterpart of the Huygens principle. In this paper, we generalize this approach to spinor wave propagation. Although the construction can be formulated on a discrete lattice of any dimension, for simplicity we focus on spinors living in 1+1 space-time dimensions. The Dirac equation in the Majorana-Weyl representation is directly recovered by incorporating appropriate symmetries of the elementary processes. The Dirac equation in the standard representation is also obtained by using its relationship with the Majorana-Weyl representation.