Conformal invariance for non-relativistic field theory

Momentum space Ward identities are derived for the amputated pi-point Green 's functions in 3+1 dimensional non-relativistic conformal field theory. Fo r n = 4 and 6 the implications for scattering amplitudes (i.e. on-shell amp utated Green's functions) are considered. Any scale invariant 2-to-2 scatte ring 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 scal e invariant. As an explicit example of a conformally invariant theory we co nsider non-relativistic particles in the infinite scattering length limit. (C) 2000 Published by Elsevier Science B.V. All rights reserved.