Resolvent operator of maxwell equations for 6-dimentional field vector

To consider problems with parameters that change in time it needs to solve the time domain Maxwell´s equations. If a medium is inhomogeneous than a problem becomes the initial and boundary value one. To solve such a problem it is convenient to transform the differential equations into integral equation, which contain initial and boundary conditions. This transformation can be done by virtue of the Green´s function for the Maxwell equations. The advantages of the Maxwell equation Green´s function over the Helmholtz and wave equation Green´s functions are that it is a single compact expression governing radiation from any source. It is needed for a description of transient electromagnetic phenomena because such phenomena are characterized as a rule by 6D vector combining electric and magnetic fields. It is especially important for time-varying medium when constitutive laws connect these fields.