Off- and On-Shell Analyticity of Three-Particle Scattering Amplitudes

Abstract

Off-shell analytic properties are obtained for amplitudes which satisfy approximate three-body equations of the Faddeev-Lovelace type. These properties are used to construct an explicit representation for the off-shell three-particle amplitude in terms of the solution of a new integral equation. The advantages of this new equation for both analytical and computational purposes are discussed, and the representation is used to determine on-shell analyticity for the amplitude. The form of the representation is such that the important three-body singularities are exhibited in a particularly transparent fashion.