  The article deals with electrodynamics in the presence of anisotropic
materials having scalar wave impedance. Maxwell's equations written for
differential forms over a 3-manifold are analysed. The system is extended to a
Dirac type first order elliptic system on the Grassmannian bundle over the
manifold. The second part of the article deals with the dynamical inverse
boundary value problem of determining the electromagnetic material parameters
from boundary measurements. By using the boundary control method, it is proved
that the dynamical boundary data determines the electromagnetic travel time
metric as well as the scalar wave impedance on the manifold. This invariant
result leads also to a complete characterization of the non-uniqueness of the
corresponding inverse problem in bounded domains of R^3.
  AMS-classifications: 35R30, 35L20, 58J45

Analysis of PDEs