  This is the first in a series of two papers (I and II), in which we revisit
the problem of decoherence in weak localization. The basic challenge addressed
in our work is to calculate the decoherence of electrons interacting with a
quantum-mechanical environment, while taking proper account of the Pauli
principle. First, we review the usual influence functional approach valid for
decoherence of electrons due to classical noise, showing along the way how the
quantitative accuracy can be improved by properly averaging over closed (rather
than unrestricted) random walks. We then use a heuristic approach to show how
the Pauli principle may be incorporated into a path-integral description of
decoherence in weak localization. This is accomplished by introducing an
effective modification of the quantum noise spectrum, after which the
calculation proceeds in analogy to the case of classical noise. Using this
simple but efficient method, which is consistent with much more laborious
diagrammatic calculations, we demonstrate how the Pauli principle serves to
suppress the decohering effects of quantum fluctuations of the environment, and
essentially confirm the classic result of Altshuler, Aronov and Khmelnitskii
for the energy-averaged decoherence rate, which vanishes at zero temperature.
Going beyond that, we employ our method to calculate explicitly the leading
quantum corrections to the classical decoherence rates, and to provide a
detailed analysis of the energy-dependence of the decoherence rate. The basic
idea of our approach is general enough to be applicable to decoherence of
degenerate Fermi systems in contexts other than weak localization as well. --
Paper II will provide a more rigorous diagrammatic basis for our results, by
rederiving them from a Bethe-Salpeter equation for the Cooperon.
