Lorentz Poles and Bethe-Salpeter Equations: Does an Infinite Number of Lorentz Poles Exist?

The possibility of the existence of an infinite family of Lorentz poles is investigated using a dynamical model. For spinless scalar particles (mass $m$) scattering via the exchange of another spinless scalar particle (mass $\mu$), the Bethe-Salpeter equation is solved in two limiting cases, $\mu =0\mathrm{}$ and $\mu \to \infty$. In both cases it is shown that the $O\left(4\right)\mathrm{}$ projected amplitude is meromorphic in $n$ (the four-dimensional angular momentum) and that there are an infinite number of poles in the $n$ plane.