  We study the influence of spin on the quantum interference of interacting
electrons in a single-channel disordered quantum wire within the framework of
the Luttinger liquid (LL) model. The nature of the electron interference in a
spinful LL is particularly nontrivial because the elementary bosonic
excitations that carry charge and spin propagate with different velocities. We
extend the functional bosonization approach to treat the fermionic and bosonic
degrees of freedom in a disordered spinful LL on an equal footing. We analyze
the effect of spin-charge separation at finite temperature both on the spectral
properties of single-particle fermionic excitations and on the conductivity of
a disordered quantum wire. We demonstrate that the notion of weak localization,
related to the interference of multiple-scattered electron waves and their
decoherence due to electron-electron scattering, remains applicable to the
spin-charge separated system. The relevant dephasing length, governed by the
interplay of electron-electron interaction and spin-charge separation, is found
to be parametrically shorter than in a spinless LL. We calculate both the
quantum (weak localization) and classical (memory effect) corrections to the
conductivity of a disordered spinful LL. The classical correction is shown to
dominate in the limit of high temperature.
