The hypothetical particles dyons, which carry both electric and magnetic charges simultaneously, are widely discussed in application to electromagnetic theory and magnetohydrodynamics. Particularly, the duality-invariant field equations were suggested with suitable definitions of the dyon's electromagnetic characteristics. In this study, we propose an alternative formulation of the duality-invariant field equations for dyons based on octonion algebra. Octonions have been used to express the equations for potentials, field strengths, and sources in a more compact and consistent manner.Additionally, the octonionic form of the energy conservation law for dyons has been derived.

This paper begins with the introduction of biquaternion algebra and its properties in compact, profound and comprehensible approach. The Schrödinger equation including both the scalar Aharonov-Bohm(sAB) and Aharonov-Casher(AC) effects, that are currently popular in particle physics and condensed-matter physics, has been rewritten by biquaternions. The newly biquaternionic Schrödinger equation, which is defined with various assumptions and approaches, also includes the biquaternionic generalized momentum in Hamiltonian.

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