Toward a manifestly causal approach to particle scattering

We introduce a new, probability-level approach to calculations in scalar field particle scattering. The approach involves the implicit summation over final states, which makes causality manifest since retarded propagators emerge naturally. Novel diagrams represent algebraic terms at the probability level, akin to Feynman diagrams at the amplitude level. We conjecture a list of rules that generate all probability-level diagrams for particle scattering processes in which one is fully inclusive over final states that contain no initial-state particles. These rules are confirmed using some fixed-order examples. The inclusivity and causal structure of this formalism may offer insights into the cancellation of infrared divergences if applied to gauge theory calculations.