Mehen, T; Stewart, IW; Wise, MB, *Conformal Invariance for Non-Relativistic Field Theory*,
Phys. Lett. B, vol. 474
(2000),
pp. 145-152 .
**Abstract:**

*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.*