  The paper discusses the Berry phase influence on the weak localization
phenomenon at the adiabatic backscattering of ultrarelativistic particles in a
random medium. We demonstrate that bosons that pass along a certain closed path
in opposite directions come back always in phase (an example: the
backscattering enhancement of electromagnetic waves), whereas fermions come
exactly in antiphase. This produces a "complete weak antilocalization" of
ultrarelativistic fermions: the backscattering field intensity vanishes.
