  A new formulation of quantum mechanics based on differential commutator
brackets is developed. We have found a wave equation representing the fermionic
particle. In this formalism, the continuity equation mixes the Klein-Gordon and
Schrodinger probability density while keeping the Klein -Gordon and Schrodinger
current unaltered. We have found time and space transformations under which
Dirac's equation is invariant. The invariance of Maxwell's equations under
these transformations shows that the electric and magnetic fields of a moving
charged particle are perpendicular to the velocity of the propagating particle.
This formulation agrees with the quaternionic formulation recently developed by
Arbab.
