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### Classical formulation

Let us denote the density of electric current by , the electric field by , the electric displacements by , the magnetic field by  and the magnetic induction by . Then are valid in a domain  the following laws:
where  is the velocitiy of the light in vacuum and  the electric charge density. A coupling with constitutive laws leads to
where  is a monotonic function and has for instance to represent the behaviour of soft iron for high field saturation. The function  is a given electric source. In so-called chiral materials is assumed the Drude-Born-Fedorov constitutive law. Let be  the electric permittivity,  the magnetic permeability,  the chirality measure then the constitutive relations read as follows:

After a simple calculation one can find in case of an achiral material with constants  and :

In an isotropic chiral medium an has the socalled Tellegen representation :
In a source-free region we have

Sometimes one has . Often the displacement current term  can be neglected. Then the equation simplifies.

A late reference: Augusto Visintin, (1996) Models of Phase transitions, Progress in Nonlinear Differential Equations and their Applications, Volume 28, Birkhäuser Basel.

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collected and worked out by Wolfgang Sprößig, TU-Bergakademie Freiberg