  Weak-interaction currents are studied in a recently proposed effective field
theory of the nuclear many-body problem. The Lorentz-invariant effective field
theory contains nucleons, pions, isoscalar scalar ($\sigma$) and vector
($\omega$) fields, and isovector vector ($\rho$) fields. The theory exhibits a
nonlinear realization of $SU(2)_L \times SU(2)_R$ chiral symmetry and has three
desirable features: it uses the same degrees of freedom to describe the
axial-vector current and the strong-interaction dynamics, it satisfies the
symmetries of the underlying theory of quantum chromodynamics, and its
parameters can be calibrated using strong-interaction phenomena, like hadron
scattering or the empirical properties of finite nuclei. Moreover, it has
recently been verified that for normal nuclear systems, it is possible to
systematically expand the effective lagrangian in powers of the meson fields
(and their derivatives) and to reliably truncate the expansion after the first
few orders. Here it is shown that the expressions for the axial-vector current,
evaluated through the first few orders in the field expansion, satisfy both
PCAC and the Goldberger--Treiman relation, and it is verified that the
corresponding vector and axial-vector charges satisfy the familiar chiral
charge algebra. Explicit results are derived for the Lorentz-covariant,
axial-vector, two-nucleon amplitudes, from which axial-vector meson-exchange
currents can be deduced.
