A Soluble Problem in Dispersion Theory

The Lee model is modified by addition of a new field ${\theta }^{\prime }$ and a weak coupling $N+\theta \to N+{\theta }^{\prime }$, which leads to instability of the $V$ particle: $V\to N+\theta \to N+{\theta }^{\prime }$. The decay amplitude is calculated to lowest order in the weak coupling by dispersion relation methods. In effect we are required to study a set of simultaneous dispersion relations. The problem is completely soluble and serves to clarify the essential structure of dispersion methods. The results agree with what one obtains, more easily in the present case, by direct methods.