Integral Equations for the Transition Matrices in the Static Meson Theory

The Chew-Low-Wick integral equation for the scattering matrix in the static meson theory has been generalized so as to make it possible to treat the various pion processes in which arbitrary numbers of pions are involved. Such a generalization is also necessitated if one wants to take into account the contribution of two- or more-meson configurations in pion-nucleon scattering. The outgoing or incoming wave functions corresponding to the many-meson initial states are defined in the same manner as by the above-mentioned authors in the one-meson problem, and are shown to be identical with those introduced by Lippmann and Schwinger. An approximate expression for the two-meson production matrix is obtained and some correction terms due to this production are derived for the Chew-Low one-meson equation.