A New Wave Quantum Relativistic Equation from Quaternionic Representation of Maxwell-Dirac Isomorphism as an Alternative to Barut-Dirac Equation

Abstract

It is known that Barut's equation could predict lepton and hadron mass with remarkable precision. Recently some authors have extended this equation, resulting in Barut-Dirac equation. In the present article we argue that it is possible to derive a new wave equation as alternative to Barut-Dirac's equation from the known exact correspondence (isomorphism) between Dirac equation and Maxwell electromagnetic equations via biquaternionic representation. Furthermore, in the present note we submit the viewpoint that it would be more conceivable if we interpret the vierbein of this equation in terms of
superfluid velocity, which in turn brings us to the notion of topological electronic liquid. Some implications of this proposition include quantization of celestial systems. We also argue that it is possible to find some signatures of Bose-Einstein cosmology, which thus far is not explored
sufficiently in the literature. Further experimental observation to verify or refute this proposition
is recommended.