  We calculate the electronic resistivity of a GaAs-based semiconductor quantum
wire in the presence of acoustic phonon scattering. We find that the usual
Drude-Boltzmann transport theory leads to a low temperature activated behavior
instead of the well-known Bloch-Gr\"uneisen power law. Many-body
electron-phonon renormalization, which is entirely negligible in higher
dimensional systems, has a dramatic effect on the low temperature quantum wire
transport properties as it qualitatively modifies the temperature dependence of
the resistivity from the exponentially activated behavior to an approximate
power law behavior at sufficiently low temperatures.
