  Parity-violating quasielastic electron scattering is studied within the
context of the relativistic Fermi gas and its extensions to include the effects
of pionic correlations and meson-exchange currents. The work builds on previous
studies using the same model; here the part of the parity-violating asymmetry
that contains axial-vector hadronic currents is developed in detail using those
previous studies and a link is provided to the transverse vector-isovector
response. Various integrated observables are constructed from the differential
asymmetry. These include an asymmetry averaged over the quasielastic peak, as
well as the difference of the asymmetry integrated to the left and right of the
peak -- the latter is shown to be optimal for bringing out the nature of the
pionic correlations. Special weighted integrals involving the differential
asymmetry and electromagnetic cross section, based on the concepts of y-scaling
and sum rules, are constructed and shown to be suited to studies of the
single-nucleon form factor content in the problem, in particular, to
determinations of the isovector/axial-vector and electric strangeness form
factors. Comparisons are also made with recent predictions made on the basis of
relativistic mean-field theory.
