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.
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