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 subatomic particles scatter off each other, they typically use Feynman diagrams, a powerful visual language invented by Richard Feynman in the 1940s. But these standard diagrams work at the level of quantum amplitudes, which don’t directly enforce the rule that causes must come before effects.
This paper introduces a new kind of diagram that works at the level of probabilities instead. By summing over all the possible outcomes of a collision in a specific way, our formalism naturally produces mathematical objects called “retarded propagators”, quantities that automatically respect causality. We lay out a conjectured set of rules for drawing these new diagrams for any scattering process, creating a toolkit that could complement or simplify the traditional Feynman approach. Because the formalism works directly with physical (measurable) quantities rather than intermediate amplitudes, it may also shed light on how certain mathematical infinities cancel in more realistic theories, a long-standing puzzle in particle physics.
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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