  In many strongly correlated electron systems, remarkable violation of the
relaxation time approximation (RTA) is observed. The most famous example would
be high-Tc superconductors (HTSCs), and similar anomalous transport phenomena
have been observed in metals near their antiferromagnetic (AF) quantum critical
point (QCP). Here, we develop a transport theory involving resistivity and Hall
coefficient on the basis of the microscopic Fermi liquid theory, by considering
the current vertex correction (CVC). In nearly AF Fermi liquids, the CVC
accounts for the significant enhancements in the Hall coefficient,
magnetoresistance, thermoelectric power, and Nernst coefficient in nearly AF
metals. According to the numerical study, aspects of anomalous transport
phenomena in HTSC are explained in a unified way by considering the CVC,
without introducing any fitting parameters; this strongly supports the idea
that HTSCs are Fermi liquids with strong AF fluctuations. In addition, the
striking \omega-dependence of the AC Hall coefficient and the remarkable
effects of impurities on the transport coefficients in HTSCs appear to fit
naturally into the present theory. The present theory also explains very
similar anomalous transport phenomena occurring in CeCoIn5 and CeRhIn5, which
is a heavy-fermion system near the AF QCP, and in the organic superconductor
\kappa-(BEDT-TTF).
