A discrete model of the Dirac-Kähler equation

We construct a new discrete analogue of the Dirac–Kähler equation in which some key geometric aspects of the continuum counterpart are captured. We describe a discrete Dirac–Kähler equation in the intrinsic notation as a set of difference equations and prove several statements about its decomposition into difference equations of Duffin type. We study an analogue of gauge transformations for the massless discrete Dirac–Kähler equations.