A NEW CONSTRUCTION FOR SPINOR WAVE-EQUATIONS

The construction of discrete scalar wave propagation equations in arbi trary inhomogeneous media was recently achieved by using elementary dy namical processes realizing a discrete counterpart of the Huygens prin ciple. In this paper, we generalize this approach to spinor wave propa gation. Although the construction can be formulated on a discrete latt ice of any dimension, for simplicity we focus on spinors living in 1 1 space-time dimensions. The Dirac equation in the Majorana-Weyl repr esentation is directly recovered by incorporating appropriate symmetri es of the elementary processes. The Dirac equation in the standard rep resentation is also obtained by using its relationship with the Majora na-Weyl representation.