  The main goal of this paper is to adopt a multivector calculus scheme to
study finite difference discretizations of Klein-Gordon and Dirac equations for
which Chebyshev polynomials of the first kind may be used to represent a set of
solutions. The development of a well-adapted discrete Clifford calculus
framework based on spinor fields allows us to represent, using solely
projection based arguments, the solutions for the discretized Dirac equations
from the knowledge of the solutions of the discretized Klein-Gordon equation.
Implications of those findings on the interpretation of the lattice fermion
doubling problem is briefly discussed.
