  Momentum space Ward identities are derived for the amputated n-point Green's
functions in 3+1 dimensional non-relativistic conformal field theory. For n=4
and 6 the implications for scattering amplitudes (i.e. on-shell amputated
Green's functions) are considered. Any scale invariant 2-to-2 scattering
amplitude is also conformally invariant. However, conformal invariance imposes
constraints on off-shell Green's functions and the three particle scattering
amplitude which are not automatically satisfied if they are scale invariant. As
an explicit example of a conformally invariant theory we consider
non-relativistic particles in the infinite scattering length limit.
