S-Matrix Singularity Structure in the Physical Region. III. General Discussion of Simple Landau Singularities

Abstract

Drawing on the understanding of unitarity integrals acquired in previous papers [J. Math. Phys. 10, 494, 545 (1969)], we show that unitarity demands that connected amplitudes be singular on the positive-α arcs of all ``simple'' Landau curves in their physical regions. Further, we show that the amplitudes are nonsingular on mixed-α arcs, while on the positive-α arcs their discontinuities are given by the Cutkosky rule. This confirms arguments from perturbation theory and demonstrates how a weak analyticity assumption can generate in an exact way a singularity scheme relating to causality.