  We describe consequences of the chiral anomaly in the theory of quantum
wires, the (quantum) Hall effect, and of a four-dimensional cousin of the Hall
effect. We explain which aspects of conductance quantization are related to the
chiral anomaly. The four-dimensional analogue of the Hall effect involves the
axion field, whose time derivative can be interpreted as a (space-time
dependent) difference of chemical potentials of left-handed and right-handed
charged fermions. Our four-dimensional analogue of the Hall effect may play a
significant role in explaining the origin of large magnetic fields in the
(early) universe.
