Faddeev Equations in the Functional Quantum Theory of the Non-Linear Spinorfield

Abstract

Abstract Starting with a linear partial differential operator for a certain system of transition amplitudes associated to a state |a> with baryon number ρ(a) we derive an equation in the ρ(a)-sector of the Functional space which provides the state |a> with an effective potential caused by the polarization cloud. With regard to the needs of n-body scattering we then undertake a cluster decomposition of the effective potential. In particular, we derive the relativistic analoga of Lippmann-Schwinger-and Faddeev equations.