  In the rest frame of the nucleus, shadowing is due to hadronic fluctuations
of the incoming virtual photon, which interact with the nucleons. We expand
these fluctuations in a basis of eigenstates of interaction and take only the
$q\bar q$ component of the hadronic structure of the photon into account. We
use a representation in which the $q\bar q$-pair has a definite transverse
size. Starting from the Dirac equation, we develop a path integral approach
that allows to sum all multiple scattering terms and accounts for fluctuations
of the transverse size of the pair, as well as for the finite lifetime of the
hadronic state. First numerical results hep-ph/9807211 have shown that higher
order scattering terms have a strong influence on the total cross section
$\sigma^{\gamma^*A}_{tot}$. The aim of this paper is to give a detailed
derivation of the formula for the total cross section.
