The Nucleon and the Roper Resonance

A coupled two-channel bootstrap calculation is performed for the static system of $\pi N$ and $\pi \pi N$ states in the positive-parity $I=J=\frac{1}{2}$ state. For the $\pi \pi N$ state, we use an analysis of Ball et al. which reduces the three-particle system to a two-particle system with a modified phase space. The calculations are made using the $\frac{N}{D}$ method and the static Bethe-Salpeter equation. The results are in reasonable agreement with the experimental positions and partial widths, and imply that the Roper resonance is primarily a $\pi \pi N$ resonance.