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The European Physical Journal B
ISSN: 1434-6028 (printed version)
ISSN: 1434-6036 (electronic version)
Abstract Volume 3 Issue 4 (1998) pp 517-534
A new construction for spinor wave equations
S. de Toro Arias (1)(2) (a), C. Vanneste (1) (b)
(1) Laboratoire de Physique de la Matière Condensée (CNRS UMR 6622), Université de Nice-Sophia Antipolis, Parc Valrose, B.P. 71, 06108 Nice Cedex 02, France
(2) Service de Physique de l'État Condensé, Centre d'Études de Saclay, l'Orme des Merisiers, 91191 Gif-sur-Yvette Cedex, France
Received: 3 November 1997 / Received in final form: 9 February 1998 / Accepted: 16 February 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.
PACS. 03.65.Pm Relativistic wave equations - 02.70.-c Computational techniques
(a) email: sdetoro@spec.saclay.cea.fr
(b) email: vanneste@ondine.unice.fr
Article in PDF-Format (747 KB)
Online publication: July 22, 1998
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