Tensor Formulation of Dirac Equation in Standard Representation

In previous works, via Cartan map, Dirac equation for half-spin particle has been written in tensor form by using the spinor representation of Dirac matrices. However, it is well known that, there exist different representations of Dirac matrices. The most used representations are the standard and the spinor representations. It has been proved that, Dirac equation written in tensor form by using the spinor representation takes the form of non-linear Maxwell's like equations for two electromagnatic fields ( E,H ) and ( E',H' ). To compare the results of both the spinor and the standard representations, in this work, we wrote Dirac equation in tensor form, using the standard representation.