On the Relativistic Description of the Multichannel γp Scattering Reactions in the Framework of the Three-Body Field-Theoretical Equations

Abstract

A new form of the relativistic three-body equations for the coupled πN and γN scattering reactions with three particle final states ππN and γπN is suggested. These equations are derived in the framework of the time-ordered three dimensional field theory. The solutions of the considered equations satisfy the unitarity condition and are exactly gauge invariant. The form of the suggested three-body equations is not dependent on the choice of the model Lagrangian, and this form is also the same for the formulations with and without quark degrees of freedom. The effective potentials of these equations are defined by the vertex functions with two on-mass shell particles.The used formulation of the relativistic three-dimensional and three-body equations allows us to overcome a number of approximations which are usually used by practical calculations of the πN and γN scattering reactions.