Causality as an emergent macroscopic phenomenon: The Lee-Wick O(N) model

In quantum mechanics the deterministic property of classical physics is an emergent phenomenon appropriate only on macroscopic scales. Lee and Wick introduced Lorentz invariant quantum theories where causality is an emergent phenomenon appropriate for macroscopic time scales. In this paper we analyze a Lee-Wick version of the O(N) model. We argue that in the large N limit this theory has a unitary and Lorentz invariant S matrix and is therefore free of paradoxes in scattering experiments. We discuss some of its acausal properties.