Generalized Klein-Gordon field equations with octonion space-time (OST) algebra

The concept of space-time representation is redefined using the octonion space-time (OST) algebra. In this study, describing the properties of octonions and their possible connection with Euclidean space-times, the internal and external space-time events are represented within the OST algebra. Keeping in mind the octonionic dual-Euclidean space-times, we express the homogeneous field equations which leads to the symmetrical nature of internal and external space-times. We derive the generalized Proca-Maxwell equations for massive-dyons in the case of the OST algebra. Accordingly, we have obtained a new set of octonionic Klein-Gordon potential (KGP) and Klein-Gordon field (KGF) equations for massive dyons from the generalized Proca-Maxwell equations. This formalism demonstrates that the octonionic KGP and KGF equations can be expressed in a single equation and it is equivalent to energy-momentum relation for dyons. As such, we have made an attempt to write the conservation of Noetherian current from the octonionic Klein-Gordon equations.