  We have studied electroweak (EW) interactions in quantum hadrodynamics (QHD)
effective field theory (EFT). The Lorentz-covariant EFT contains nucleon, pion,
$\Delta$, isoscalar scalar ($\sigma$) and vector ($\omega$) fields, and
isovector vector ($\rho$) fields. The lagrangian exhibits a nonlinear
realization of (approximate) $SU(2)_L \otimes SU(2)_R$ chiral symmetry and
incorporates vector meson dominance. First, we discuss the EW interactions at
the quark level. Then we include EW interactions in QHD EFT by using the
background-field technique. The completed QHD EFT has a nonlinear realization
of $SU(2)_L \otimes SU(2)_R \otimes U(1)_B$ (chiral symmetry and baryon number
conservation), as well as realizations of other symmetries including
Lorentz-invariance, $C$, $P$, and $T$. Meanwhile, as we know, chiral symmetry
is manifestly broken due to the nonzero quark masses; the $P$ and $C$
symmetries are also broken because of weak interactions. These breaking
patterns are parameterized in a general way in the EFT. Moreover, we have
included the $\Delta$ resonance as manifest degrees of freedom in our QHD EFT,
with a discussion of the irrelevance of the well-known pathologies involving
high-spin fields from the modern EFT perspective. This enables us to discuss
physics at the kinematics where the resonance becomes important. As a result,
the effective theory uses hadronic degrees of freedom, satisfies the
constraints due to QCD (symmetries and their breaking pattern), and is
calibrated to strong-interaction phenomena. Applications to (anti)neutrino
scattering are briefly discussed.
