  The dynamical equations of an electromagnetic field coupled with a conducting
material are studied. The properties of the interaction are described by a
classical field theory with tensorial material laws in space-time geometry. We
show that the main features of superconducting response emerge in a natural way
within the covariance, gauge invariance and variational formulation
requirements. In particular, the Ginzburg-Landau theory follows straightforward
from the London equations when fundamental symmetry properties are considered.
Unconventional properties, such as the interaction of superconductors with
electrostatic fields are naturally introduced in the geometric theory, at a
phenomenological level. The BCS background is also suggested by macroscopic
fingerprints of the internal symmetries.
  It is also shown that dissipative conducting behavior may be approximately
treated in a variational framework after breaking covariance for adiabatic
processes. Thus, nonconservative laws of interaction are formulated by a purely
spatial variational principle, in a quasi-stationary time discretized
evolution. This theory justifies a class of nonfunctional phenomenological
principles, introduced for dealing with exotic conduction properties of matter
[Phys. Rev. Lett. 87, 127004 (2001)].
