Stability of the scalar chi(2)phi interaction - art. no. 076008

A scalar field theory with a chi (dagger)chi phi interaction is known to be unstable. Yet it has been used frequently without any sign of instability in standard textbook examples and research articles. In order to reconcile these seemingly conflicting results, we show that the theory is stable if t he Fock space of all intermediate states is limited to a finite number of c losed <<chi>(chi )over bar>loops associated with a field chi that appears q uadradically in the interaction, and that instability arises only when inte rmediate states include these loops to all orders. In particular, the quenc hed approximation is stable.