  We consider the problem of calculating the Green's functions associated to a
massive scalar field with modified dispersion relations. We analyze the case
when dispersion is modified by higher derivative spatial operators acting on
the field orthogonally to a preferred direction, determined by a unit time-like
vector field. By assuming that the integral curves of the vector field are
geodesics, we expand the modified Klein-Gordon equation in Fermi normal
coordinates. By means of a Fourier transform, we find a series representation
in momentum-space of the Green's functions. The coefficients of the series are
geometrical terms containing combinations of the Ricci tensor and the vector
field, as expected from previous calculations with different methods and for
specific backgrounds.
