  We theoretically study the spin dynamics in antiferromagnets (AFs)under the
influence of an electric current. We identify two different sources of
spin-transfer torques that stem from uniform (${\boldsymbol v}_n$) and
staggered (${\boldsymbol v}_\ell$) electron spin densities. While the former is
well recognized, the latter is often overlooked. We show that both
${\boldsymbol v}_n$ and ${\boldsymbol v}_\ell$ contribute equally to the
spin-wave Doppler shift. Microscopic calculations are presented for electrons
on a two-dimensional square lattice with nearest-neighbor ($t$) and
next-nearest-neighbor ($t'$) hopping, which interpolate two opposite transport
regimes of strongly-coupled AF ($t'/t \ll 1$) and two weakly coupled
ferromagnets ($t'/t \gg 1$). In the AF transport regime ($t'/t \ll 1$),
${\boldsymbol v}_n$ and ${\boldsymbol v}_\ell$ have opposite signs, and the
sign of the Doppler shift depends on band filling; ${\boldsymbol v}_n$
(${\boldsymbol v}_\ell$) is dominant near the AF gap (near the band bottom or
the top). As $t'/t$ is increased, ${\boldsymbol v}_n$ undergoes a sign change
whereas ${\boldsymbol v}_\ell$ does not. In the limit of vanishing $t$,
${\boldsymbol v}_n$ and ${\boldsymbol v}_\ell$ coincide and the spin-transfer
torque reduces to that of ferromagnets.
