Landau-Lifshitz theory of single susceptibility Maxwell equations

Abstract

The conflicting arguments given in the discussion forum of Metamaterials 2011 on the possible forms of macroscopic Maxwell equations are lead to a convergence by noting the relationship among the employed material variables for each scheme. The three schemes by Chipouline et al. using (A) standard $\Vec{P}$ and $\Vec{M}$ (Casimir form), (B) generalized electric polarization $\Vec{P}_{LL}$ (Landau-Lifshitz form), (C) generalized magnetic polarization $\Vec{M}_{A}$ (Anapole form) are compared with (D) the present author's scheme using standard current density $\Vec{J}$. From the reversible relations among the transverse components of these vectors, one can easily rewrite one scheme into another. The scheme (D), the only one among the four providing the first-principles expressions of susceptibility and also leading to a non-phenomenological Casimir form in terms of the four generalized susceptibilities between $\{\Vec{P},\Vec{M}\}$ and $\{\Vec{E},\Vec{B}\}$, is concluded to be a more natural form than (B) and (C) as a single susceptibility theory.