Relativistic Three-Pion Calculation. I

In order to do a reasonably simple relativistic three-meson calculation, we examine a relativistic analog to the Faddeev equations proposed by Alessandrini and Omnes. An explicit angular-momentum decomposition, following the method of Omnes, is given. Some remarks are made about suitable approximations for the relativistic off-shell two-body amplitude, and a separable form of this is used to reduce the equations to their final form. As an example, the explicit equations are written in the three-pion $I=0\mathrm{}$, $J^p=1^{-}$ case.