Model-independent derivation of macroscopic Maxwell equations from microscopic basis: Defects of ”E,D,B,H” scheme

The derivation of macroscopic Maxwell equations (M-eqs.) from microscopic basis is made in a general, model-independent way. Starting from a general Lagrangian of interacting matter-EM field as a most reliable basis, we first set up simultaneous equations for microscopic ”EM field and induced current density”, where a single (microscopic) susceptibility tensor is enough to describe the whole response. Macroscopic averaging is done by applying long wavelength approximation to the microscopic response, which results in a new but familiar form of macroscopic ”constitutive equation”. This procedure does not increase the number of field variables, neither the number of consitutive equation. This form of macroscopic M-eqs. is not equivalent to the usual {E,D,B,H} scheme, which requires two constitutive equations. Plane wave dispersion equation takes a different form, and an alteration is required to the definition (ǫ < 0, μ < 0) of left-handed materials. An experimental test is proposed to distinguish this and the traditional forms of macroscopic M-eqs.