  A generalized Peierls substitution which takes into account a Berry phase
term must be considered for the semiclassical treatment of electrons in a
magnetic field. This substitution turns out to be an essential element for the
correct determination of the semiclassical equations of motion as well as for
the semiclassical Bohr-Sommerfeld quantization condition for energy levels. A
general expression for the cross-sectional area is derived and used as an
illustration for the calculation of the energy levels of Bloch and Dirac
electrons.
