Toward a manifestly causal approach to particle scattering
Published in Physical Review D, 2025
Abstract
We introduce a probability-level formalism for calculating particle scattering in scalar field theory. The approach features implicit summation over final states, which naturally makes causality manifest by producing retarded propagators. Rather than using traditional Feynman diagrams at the amplitude level, the work introduces new diagram types that represent algebraic terms at the probability level. We conjecture a set of rules generating all probability-level diagrams for particle scattering processes with full inclusivity over final states containing no initial-state particles. The inclusivity and causal structure of this formalism may provide insights into the cancellation of infrared divergences when applied to gauge theory calculations.
Layman’s Abstract
When physicists calculate how particles scatter off each other, they usually work with mathematical objects that don’t explicitly respect the rule that cause must precede effect. This paper develops a new approach where causality is built in from the start. By summing over all possible outcomes in a particular way, we obtain calculations that naturally use “retarded” propagators – mathematical tools that ensure effects only propagate forward in time. The new method may also help explain how certain infinities cancel out in more complex theories.
Links
- Physical Review D
- arXiv:2502.18551 (extended version)
- InspireHEP
Recommended citation: Dickinson, R., Forshaw, J., Jenkinson, R., & Millington, P. (2025). "Toward a manifestly causal approach to particle scattering." Physical Review D.
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