Perturbation theory for relativistic Lee model (Q1078777)

A fully relativistic version of the Lee model is considered where three scalar bosons called N, \(\theta\) and V interact according to the scheme \(N+\theta \leftrightarrow V\). It is shown that if one accepts an assumption suggested by the Birman-Kato invariance principle, the asymptotic problem of this model can be solved and the S-matrix elements can be written as convergent series using Dyson-like perturbation methods. The renormalization is done before computing the terms of the S- matrix elements.