Feshbach-Villars formalism and pion-nucleon scattering

Abstract

The Feshbach-Villars Hamiltonian formulation of the Klein-Gordon equation is used as the basis for a scattering theory for relativistic, spin-zero, particles. Time dependent and time independent scattering theories are developed. The time independent theory is used as the framework for a separable potential model for $\pi N$ elastic scattering in $P$ waves. This potential leads to a $\pi N$ $T$ matrix which has the right and left hand cuts associated with two-particle unitarity and crossing, respectively, as well as the direct and crossed nucleon poles with the proper residues. The effects of nucleon recoil are included. With a particular choice of the form factors in the potential, the Chew-Low $T$ matrix is reproduced.