  We study optical conductivities for high-Tc superconductors under the
magnetic field on the basis of the microscopic Fermi liquid theory. Current
vertex corrections (CVC's) are correctly taken into account to satisfy the
conservation laws, which has been performed for the first time for optical
conductivities based on the fluctuation-exchange (FLEX) approximation. We find
that the CVC emphasizes the $\omega$-dependence of $\sigma_{xy}(\omega)$
significantly when the antiferromagnetic (AF) fluctuations are strong. By this
reason, the relation $\sigma_{xy}(\omega) \sim {\sigma(\omega)}^2$, which is
satisfied in the extended-Drude model given by the relaxation time
approximation (RTA), is totally violated for a wide range of frequencies.
Consequently, the optical Hall coefficient $R_H(\omega)$ strongly depends on
$\omega$ below the infrared frequencies, which is consistent with experimental
observations. We also study the mystery about a simple-Drude form of the
optical Hall angle $\theta_H(\omega)$ observed by Drew et al., which is highly
nontrivial in terms of the RTA since the strong $\omega$-dependence of the
relaxation time should modify the Drude-form. We find that a simple Drude-form
of $\theta_H(\omega)$ is realized because the $\omega$-dependence of the CVC
almost cancels that of the relaxation time. In conclusion, anomalous optical
transport phenomena in high-Tc superconductors, which had been frequently
assumed as an evidence of the breakdown of the Fermi liquid state, are well
understood in terms of the nearly AF Fermi liquid once the CVC is taken into
account.
