Relativistic quantal three body-problem and hermeticity requirements

In the present paper, the Euler-Lagrange's differential equations that minimize, the relativistic quantal action, in the frame of the generalized calculus of variations, are established. After utilizing natural collision coordinates and insuring correct asymptotic requirements, the centre of mass is excluded. The remaining two dimensional equation of motion is provided with an effective potential function-, and reduced-spinors- which vary with the reaction coordinates, together with a boundary term that is responsible for securing its intrinsic self-adjointness. The separability of this equation into eigen-value equation and a set of coupled channel one-dimensional scattering equations are feasible. The optical model approximation is employed for squeezing the competing coupled channels into an effective single channel