  We have developed an approach to calculate the single-particle Green function
of a one-dimensional many-body system in the strongly localized limit at zero
temperature. Our approach, based on the locator expansion, sums the
contributions of all possible forward scattering paths in configuration space.
We demonstrate for fermions that the Green function factorizes when the system
can be splited into two non interacting regions. This implies that for nearest
neighbors interactions the Green function factorizes at every link connecting
two sites with the same occupation. As a consequence we show that the
conductance distribution function for interacting systems is log-normal, in the
same universality class as for non-interacting systems. We have developed a
numerical procedure to calculate the ground state and the Green function,
generating all possible paths in configuration space. We compare the
localization length computed with our procedure with the one obtained via exact
diagonalization. The latter smoothly converges to our results as the disorder
increases.
