Linear Integral Equations for Relativistic Multichannel Scattering

Abstract

A set of three-dimensional coupled linear integral equations is presented for relativistic scattering and production processes. The new equations seem more amenable to numerical analysis than the standard Bethe-Salpeter equations. In addition one may discuss multiparticle scattering and hence inelastic processes. As a numerical example we discuss low-energy pion-pion scattering in the simplest approximation. We find that there are no self-consistent values for the mass and width of the $\rho$ meson if one takes into account only the elastic and $\pi -\omega$ channels.