Quaternion equations of electromagnetic field in isotropic homogeneous media.

In this paper, we propose a quaternion form of equations describing electromagnetic field in a homogeneous isotropic medium without dispersion. It is shown that by renormalizing the values of field inductions and sources, one can transform the asymmetrical Maxwell equations to a highly symmetric form. This provides a possibility to introduce the scalar and vector field potentials and represent the generalized equation for electromagnetic field in the form of a single second-order quaternionic wave equation. We demonstrate that this equation reduces to the system of ordinary hyperbolic wave equations for the field potentials and on the other hand, the same equation is equivalent to the system of Maxwell equations for renormalized field intensities. The symmetry of the renormalized Maxwell equations allows one to obtain the second-order relations for energy and momentum, as well as for Lorentz invariants of the renormalized fields, which formally have the same form as for the fields in a vacuum. In addition, the generalization of renormalized equations to the case of magnetic sources corresponding to the models of Dirac magnetic monopoles and Schwinger dyons is discussed. [ABSTRACT FROM AUTHOR]