Eur. Phys. J. Plus (2022) 137: 621
https://doi.org/10.1140/epjp/s13360-022-02776-7

Regular Article

Quaternion Klein–Gordon equation in the electromagnetic field

Department of Physics, Zakir Husain Delhi College (Delhi University), New Delhi, India

^a email-rawatseema1@rediffmail.com

Received: 22 March 2022
Accepted: 27 April 2022
Published online: 23 May 2022

Abstract

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.