  We analyze the effect of weak field gravitational waves on the timing of
pulsars, with particular attention to gauge invariance, that is, to the effects
that are independent of the choice of coordinates. We find: (i) the Doppler
shift cannot be separated into gauge invariant gravitational wave and kinetic
contributions; (ii) a gauge invariant separation can be made for the time
derivative of the Doppler shift in which the gravitational wave contribution is
directly related to the Riemann tensor, and the kinetic contribution is that
for special relativity; (iii) the gauge dependent effects in the Doppler shift
play no role in the program of gravitational wave detection via pulsar timing.
The direct connection shown between pulsar timing and the Riemann tensor of the
gravitational waves will be of importance in discussions of gravitational waves
from alternative (non-Einsteinian) theories of gravitation.
