Conformal Invariance for Non-Relativistic Field Theory

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.

Figures (2)

• Figure 1: Terms contributing to ${\cal A}^{(4)}$ from the interaction in Eq. (\ref{['S1']}).
• Figure 2: Terms contributing to ${\cal A}^{(6)}$ from the interaction in Eq. (\ref{['S1']}). The filled circle denotes the sum of diagrams in Fig. 1.