  A relativistic analogue of the quantum adiabatic approximation is developed
for Klein-Gordon fields minimally coupled to electromagnetism, gravity and an
arbitrary scalar potential. The corresponding adiabatic dynamical and
geometrical phases are calculated. The method introduced in this paper avoids
the use of an inner product on the space of solutions of the Klein-Gordon
equation. Its practical advantages are demonstrated in the analysis of the
relativistic Landau level problem and the rotating cosmic string.
