  The zero frequency conductivity ($D_c$), the criterion to distinguish between
conductors and insulators is expressed in terms of a geometric phase. $D_c$ is
also expressed using the formalism of the modern theory of polarization. The
tenet of Kohn [{\it Phys. Rev.} {\bf 133} A171 (1964)], namely, that insulation
is due to localization in the many-body space, is refined as follows.
Wavefunctions which are eigenfunctions of the total current operator give rise
to a finite $D_c$ and are therefore metallic. They are also delocalized.
Several examples which corroborate the results are presented, as well as a
numerical implementation. The formalism is also applied to the Hall
conductance, and the quantization condition for zero Hall conductance is
derived to be $\frac{e\Phi_B}{N h c} = \frac{Q}{M}$, with $Q$ and $M$ integers.
