  It is shown that the hypercomplex Dirac equation describes the system of
connected fields: 4-scalar, 4-pseudoscalar, 4-vector, 4-pseudo-vector and
antisymmetric 4-tensor second rank field. If mass is assumed to be zero this
system splits into two subsystems. Equations containing tensor, scalar and
pseudoscalar fields coincide with Maxwell equations complemented by scalar and
pseudoscalar fields. This system describes the electrodynamics of non-conserved
charges. The scalar and pseudoscalar fields are generated only by the
non-conserved charges - electric and hypothetical magnetic. The influence of
these fields on the charged particles is very unusual - it causes a change of
their rest mass. This allows us to give a new look at the Wigner paradox and
mechanism of mass renormalization.
