  It is known that various transport coefficients strongly deviate from
conventional Fermi-liquid behaviors in many electron systems which are close to
antiferromagnetic (AF) quantum critical points (QCP). For example, Hall
coefficients and Nernst coefficients in three-dimensional heavy fermion CeCoIn5
and CeCu6-xAux increase strikingly at low temperatures, whose overall behaviors
are similar to those in high-Tc cuprates. These temperature dependences are too
strong to explain in terms of the relaxation time approximation. To elucidate
the origin of these anomalous transport phenomena in three-dimensional systems,
we study the current vertex corrections (CVC) based on the fluctuation exchange
(FLEX) approximation, and find out decisive role of the CVC. The main finding
of the present paper is that the Hall coefficient and the Nernst coefficient
strongly increase thanks to the CVC in the vicinity of the AF QCP, irrespective
of dimensionality. We also study the relaxation time of quasi-particles, and
find that "hot points" and "cold lines" are formed in general three-dimensional
systems due to strong AF fluctuations.
