  We explore the consequences of conformal symmetry for the operator product
expansions in nonrelativistic field theories. Similar to the relativistic case,
the OPE coefficients of descendants are related to that of the primary.
However, unlike relativistic CFTs the 3-point function of primaries is not
completely specified by conformal symmetry. Here, we show that the 3-point
function between operators with nonzero particle number, where (at least) one
operator has the lowest dimension allowed by unitarity, is determined up to a
numerical coefficient. We also look at the structure of the family tree of
primaries with zero particle number and discuss the presence of conservation
laws in this sector.
