Abstract
An elementary spin-zero particle pole is inserted in the Bethe-Salpeter equation. This gives a non-Regge ${\ensuremath{\delta}}_{l0}$ term in the potential and the scattering amplitude. We present methods for calculating the $l=0$ partial-wave amplitude with emphasis on finding the pole positions. Our methods are tested with a ladder-approximation example. Finally, this puts us in a position to discuss the renormalization constants ${Z}_{1}$ and ${Z}_{{3}^{\ensuremath{'}}}$ of the elementary particle and show how the vanishing of these constants is related to bootstrap conditions.
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