  We study the implications of a change of coordinatization of momentum space
for theories with curved momentum space. We of course find that after a passive
diffeomorphism the theory yields the same physical predictions, as one would
expect considering that a simple reparametrization should not change physics.
However, it appears that general momentum-space covariance (invariance under
active diffeomorphisms of momentum space) cannot be enforced, and within a
given set of prescriptions on how the theory should encode momentum-space
metric and affine connection the physical predictions do depend on the momentum
space background. These conclusions find support in some general arguments and
in our quantitative analysis of a much-studied toy model with
maximally-symmetric (curved) momentum space.
