Title: "Premetric Classical Electrodynamics: Achievements and Prospects"


Friedrich W. Hehl and Jonathan Lux

Classical electrodynamics can be based on the conservation laws of electric charge Q and magnetic flux &Phi . Both laws are 'topological', that is, independent of the metric and the linear connection of spacetime. This framework is called premetric electrodynamics and, in order to establish a predictive theory, it requires additionally constitutive laws for the matter involved and for vacuum, respectively. The elimination of the metric in the fundamental charge and flux laws allows to formulate them only in terms of electromagnetic notions without intervention of the gravitational potential (the metric). This clear separation of concepts pays off in a more transparent structure of the fundamentals of electrodynamics and in the formulation of some applications:
(i) With a local and linear constitutive law and a ban on birefringence (Itin, Lämmerzahl, Obukhov, Rubilar, fwh), one can derive the light cone of spacetime, including its signature. The Lenz rule, the positivity of the energy of the electromagnetic field, and the Lorentz signature are irresolvably interrelated.
(ii) The linear constitutive magnetoelectric tensor can be classified à la Segrè (Schuller et al.). It allows a better classification of materials and provides insight into metamaterials (Favaro and Bergamin).
(iii) The axionic piece of the magnetoelectric tensor of Cr2O3 is non-vanishing and can be measured (Obukhov, Rivera, Schmid, fwh). Thus, the so-called Post constraint (Lakhtakia) is invalid.
(iv) The Cauchy problem can be streamlined in a premetric formulation (Perlick).
(v) The energy-momentum current can be formulated effectively and the Abraham-Minkowski controversy clarified (Obukhov).
(vi) Metamaterials can be better understood from a 4-dimensional point of view (Itin and Friedman).
(vii) The properties of the premetric Tamm-Rubilar tensor can be understood in a geometrical context as being related to generalized Fresnel-Kummer surfaces (Rubilar). These and other application will be discussed.