Causality inS-Matrix Theory

Causality conditions referring only to mass-shell quantities are formulated and some consequences are derived. A condition called weak asymptotic causality (WAC) formalizes the requirement that some interaction between initial particles must occur before the last interaction from which final particles emerge. A condition called strong asymptotic causality (SAC) formalizes the requirement that energy momentum should be carried over macroscopic distances only by physical particles. From SAC it follows that all $n$-particle scattering functions ($n>~4$) are analytic, apart from infinitely differentiable singularities, at physical points not lying on any positive-$\alpha$ Landau surface. Moreover, the scattering functions on the two sides of any such Landau surface are analytically connected by a path that passes around the singularity surface in the way prescribed by perturbation theory. Thus, apart from possible infinitely differentiable singularities, the physical-region singularity structure is derived from a mass-shell causality requirement. Several properties of positive-$\alpha$ surfaces are also discussed.