  Methods for modelling the electrical conductivity of dense plasmas and liquid
metals, based upon the well-known Ziman formula, are reviewed from a general
perspective, and some earlier inconsistencies relating to its application to
finite temperature systems are resolved. A general formula for the conductivity
of a Lorentzian two-component plasma in thermal equilibrium is derived from the
Lenard-Balescu collision integral in which both energy and momentum exchange
between ions and electrons are accounted for. This formula is used as a basis
for some generalizations of the Ziman formula, which apply to plasmas of
arbitrary degeneracy over a much wider range of conditions. These formulae
implicitly include the collective motions of the ions, but neglect the
collective motions of the electrons. Detailed consideration of the latter shows
that they generally have a small effect on the conductivity. Conditions for the
validity of the Ziman formula are derived. The extension of the general theory
to arbitrarily low temperatures, where the ion dynamics become dominated by
collective effects, in which dynamical ion correlations need to be taken into
account, is shown to lead to the well-known Bloch formula. Consideration is
given to non-Lorentzian plasmas by explicitly accounting for electron-electron
collisions. Corrections to the Lorentzian model in the form of a power series
in 1/Z are derived.
