A multivectorial Dirac equation

The multivectorial generalization of the Cartan map, for 𝒞(1,3) space-time Clifford algebra and an arbitrary gauge group in an isotopic space, is applied to the standard Dirac equation to generate the multivectorial Dirac equation. Using both geometrical and physical reasoning, a particular case discussed by Reifler and Morris [J. Math. Phys. 26, 2059 (1985)] is projected from the general multivectorial Dirac equation, to discuss the properties and limitations associated to their quaternion model. The use of the general multivectorial Dirac equation, which can be defined on any space-time manifold, is also illustrated.