Abstract
Expanding the ordinary Dirac's equation in quaternionic form yields Maxwell-like field equations. As in the Maxwell's formulation, the particle fields are represented by a scalar, psi(0) and a vector (psi) over right arrow. The analogy with Maxwell's equations requires that the inertial fields are (E) over right arrow (D) = C-2(alpha) over right arrow x ,(psi) over right arrow and (B) over right arrow (D) = (alpha) over right arrow =psi(0) + c beta(psi) over right arrow and that psi(0) = -c beta(alpha) over right arrow.(psi) over right arrow, where beta, (alpha) over right arrow and c are the Dirac matrices and the speed of light, respectively. An alternative solution suggesis that magnetic monopole-like behavior accompanies Dirac's field. In this formulation, a field like representation of Dirac's particle is derived. It is shown that when the vector field of the particle, (psi) over right arrow, is normal to the vector (alpha) over right arrow, Dirac's field represents a medium with maximal conductivity. The energy flux (Poynting vector) of the Dirac's fields is found to flow in opposite direction to the particle's motion. A system of equivalently symmetrized Maxwell's equations is introduced. A longitudinal (scalar) wave traveling at speed of light is found to accompany magnetic charges flow. This wave is not affected by presence of electric charges and currents. The Lorentz boost transformations of the matter fields are equivalent to c (psi) over right arrow' = c (psi) over right arrow +/- beta(alpha) over right arrow psi(0), (psi) over right arrow' = (psi) over right arrow = (psi) over right arrow -/+ c beta(alpha) over right arrow'.(psi) over right arrow. (C) 2017 Elsevier GmbH. All rights reserved.