  We report on the anomalous behavior of the complex conductivity of
BaFe$_{2}$As$_{2}$, which is related to the Dirac cone, in the terahertz
(THz)-frequency region. Above the spin-density-wave (SDW) transition
temperature, the conductivity spectra follow the Drude model. In the SDW state,
the imaginary part of the complex conductivity, $\sigma_2$, is suppressed in
comparison to that expected according to the Drude model. The real part,
$\sigma_1$, exhibits nearly Drude-like behavior. This behavior (i.e., almost no
changes in $\sigma_1$ and the depression of $\sigma_2$) can be regarded as the
addition of extra conductivity without any dissipations in the Drude-type
conductivity. The origin of this ultralow-dissipative conductivity is found to
be due to conductivity contribution from quasiparticles within the Dirac cone.
In other words, we are able to observe the dynamics of Dirac fermions through
the conductivity spectra of BaFe$_2$As$_2$, clearly and directly.
