  We derive a general expression for the conductivity of a disordered conductor
with electron-electron interactions (treated within the standard model) and
evaluate the weak localization correction delta sigma_{wl} employing no
approximations beyond the accuracy of the definition of delta sigma_{wl}. Our
analysis applies to all orders in the interaction and extends our previous
calculation by explicitly taking into account quantum fluctuations around the
classical paths for interacting electrons (pre-exponent). We specifically
address the most interesting low temperature limit and demonstrate that such
fluctuations can only be important in the perturbative regime of short times
while they are practically irrelevant for the Cooperon dynamics at longer
times. We fully confirm our conclusion about the existence of
interaction-induced decoherence of electrons at zero temperature for the
problem in question. We also demonstrate irrelevance of a perturbative
calculation by Aleiner et al. (AAV) [J. Low Temp. Phys. 126, 1377 (2002) and
cond-mat/0110545] and discard AAV's critique of our earlier analysis.
