On the boundary-value problems and the validity of the Post constraint in modern electromagnetism

TL;DR

This paper defends the standard boundary conditions in electromagnetism, arguing against recent proposals to modify them to exclude certain constitutive parameters, emphasizing the importance of both macroscopic and microscopic consistency.

Contribution

It demonstrates that changing boundary conditions to exclude specific constitutive parameters is inadmissible from both macroscopic and microscopic perspectives.

Findings

Standard boundary conditions are essential for consistent electromagnetism.

Proposed modifications to boundary conditions are incompatible with fundamental theory.

The paper reinforces the validity of the Post constraint in modern electromagnetism.

Abstract

We recall that the theory of electromagnetism consists of three building blocks: (a) the inhomogeneous Maxwell equations for the electric and magnetic excitations $(D,H)$ (which reflects charge conservation), (b) the homogeneous Maxwell equations for the electric and magnetic field strengths $(E,B)$ (which reflects flux conservation), and (c) the constitutive relation between $(D,H)$ and $(E,B)$. In the recent paper \cite{Lakhtakia1}, Lakhtakia proposed to change the standard boundary conditions in electrodynamics in order to exclude certain constitutive parameters. We show that this is inadmissible both from the macroscopic and the microscopic points of view.