Renormalization Constants in the Extended Lee Model (W⇄V+θ)

Abstract

The Lee model is extended to include a $W$ field with an interaction $W\ensuremath{\rightleftarrows}V+\ensuremath{\theta}$. By Green's-function techniques the model is still found to be exactly solvable in the $V\ensuremath{\theta}$ and $N\ensuremath{\theta}$ sectors; however, we present here only closed forms of the $W$ propagator and the $\mathrm{WV}\ensuremath{\theta}$ vertex function. The wave-function renormalization and the vertex-function renormalization are derived; they are not equivalent to each other, while in the Lee model they are equal.