Discussion of a Note by Federbush on Spurious Solutions of Three-Particle Equations

Federbush's recent construction of spurious homogeneous solutions of Weinberg's connected three-particle scattering equation (in a special model) is extended and generalized. The extended result is that for the special case $m_3=\infty$, $V_{12}=0\mathrm{}$, and $V_{13}$ and $V_{23}$ of unit rank, every complex energy $W$ [with $\mathrm{Im}\left(\surd W\right)\ne 0$] is an eigenvalue of the homogeneous equation, and the corresponding eigenfunctions are square integrable. The Faddeev equations corresponding to this case are examined and found not to have this deficiency. The author's opinion is that these spurious solutions of Weinberg's equation occur only in the special case noted above, and that the Weinberg equation is usable except in this case.