Resonances,metastable states and exponential decay laws in perturbation theory

Resonances which appear as perturbed bound states are discussed in the framework of Balslev-Combes theory. The corresponding metastable states are constructed using the formal perturbation expansion to orderN–1 for the (nonexistent) perturbed bound states. They are shown to have exponential decay in time governed by the complex resonance energies, up to a background of order 2N in the perturbation parameter. The results apply in lowest orderN=1 to the perturbation of bound states embedded in the continuum and in arbitrary order to cases like the Stark effect.Dedicated to Res Jost and Arthur Wightman