Quaternion Klein-Gordon equation in the electromagnetic field

A pure quaternionic Klein-Gordon equation is developed in terms of quaternion operators and wave functions. The equivalence between quaternion and covariant operators has been established while maintaining the anti-Hermitian nature of quaternion operators. We emphasize that quaternion representation is superior for relativistic quantum mechanics due to its homogeneity in four-dimensional space over (3 + 1) space-time formalism and due to its generalization. We have also obtained the equation of continuity in terms of charge density and charge current density in quaternion space, which is applicable to both particles and antiparticles and is claimed to be the true equation of continuity for relativistic quantum mechanics. Expressions for charge density and charge current density in quaternion space have been obtained, containing some additional degrees of freedom hinting toward some new particles, dark matter, or some new physical phenomenon. A pure quaternionic generalized Klein-Gordon equation for massless and massive dyons and monopoles in the electromagnetic field has been formulated by introducing four-vector gauge potentials. It has also been shown that the quaternion charge density, charge current density, and Klein-Gordon equation for dyons and monopoles are generalized expressions, and we can obtain real and complex expressions as a special case.

Automated summary

A pure quaternionic Klein-Gordon equation is developed, emphasizing the superiority of quaternion representation in relativistic quantum mechanics. The equation of continuity in quaternion space is obtained, applicable to both particles and antiparticles, and hinting towards new particles, dark matter, or new physical phenomena. Furthermore, a pure quaternionic generalized Klein-Gordon equation for massless and massive dyons and monopoles in the electromagnetic field is formulated.