  Multi-band touchings together with the emergence of fermions exhibiting
linear dispersions have recently been predicted and realized in various
materials. We first investigate the Adler-Bell-Jackiw chiral anomaly in these
multi-band touching semimetals when they are described by the pseudospin
operator in high dimensional representation. By evaluating the Chern number, we
show that the anomalous Hall effect is enhanced depending on the magnitude of
the pseudospin. It is also confirmed by the analysis of the Landau levels when
magnetic field is applied. Namely, charge pumping occurs from one multi-band
touching point to another through multi-channel Landau levels in the presence
of parallel electric and magnetic fields. We also show a pair annihilation of
two multi-band touching points by photo-irradiation. Furthermore, we propose
generalizations of Dirac semimetals, multiple-Weyl semimetals and loop-nodal
semimetals to those composed of fermions carrying pseudospins in high
dimensional representation. Finally we investigate the 3-band touching
protected by the $% C_{3}$ symmetry. We show that the 3-band touching point is
broken into two Weyl points by photo-irradiation.
