A framework to obtain wave, energy, and momentum conservation equations

Abstract A new method for obtaining wave, energy, and momentum conservation equations for Dirac and Maxwell systems is presented. This method makes use of the algebraic features of quaternion products. A framework that uses quaternions to describe quantum physics and electrodynamics has been introduced. In this approach, mass and charge produce electric and magnetic fields that satisfy Maxwell's equations. Quaternionic mass leads to massive electrodynamics based on quantum mechanics concepts. The conservation of energy and momentum is not affected by quaternionic mass. Quaternionic Maxwell's equations with quaternionic mass yield intriguing phenomena that can be examined experimentally. These equations generalize the classical Wilczek axion electrodynamics to quantum one.