Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)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. © 2015, Springer Basel.10237939913/07590-8, FAPESP, Fundação de Amparo à Pesquisa do Estado de São PauloFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Becher, P., Joos, H., The Dirac–Kähler equation and fermions on the lattice (1982) Z. Phys. 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