On the stability of one-particle states generated by quantum fields fulfilling Yang—Feldman equations

We prove that for a Wightman quantum field ∅(x) the assumptions (i) positivity of the metric on the state space of the theory, (ii) the asymptotic condition in the form of Yang—Feldman equations, and (iii) Klein—Gordon equation for the outgoing field imply that the states generated by application of the asymptotic fields to the vacuum are stable. We prove by a counterexample that this statement is wrong in the case of quantum fields with indefinite metric.