Soluble Model Field Theory with Vertex Function

Abstract

The Lee model is modified by the insertion of an elementary particle into the second sector with the coupling $U\leftrightarrow V+\theta$. The $\mathrm{UV}\theta$ vertex function, the propagators, and all the renormalization constants of the theory are evaluated exactly, and the $V\theta$ scattering amplitude is given when both incoming and outgoing $\theta$ particles are off the energy shell.