# Working directly with probabilities in quantum field theory

## TL;DR

This paper introduces a new method for calculating transition probabilities in quantum field theory directly through expectation values of nested commutators and anti-commutators, emphasizing retarded propagators and causality.

## Contribution

It presents a novel approach that bypasses squared matrix elements, providing clearer insights into causality and potential handling of infra-red divergences in quantum field theory.

## Key findings

- Diagrammatic expansion dominated by retarded propagators
- Clear demonstration of causality preventing superluminal signaling
- Potential new techniques for managing infra-red divergences

## Abstract

We present a novel approach to computing transition probabilities in quantum field theory, which allows them to be written directly in terms of expectation values of nested commutators and anti-commutators of field operators, rather than squared matrix elements. We show that this leads to a diagrammatic expansion in which the retarded propagator plays a dominant role. As a result, one is able to see clearly how faster-than-light signalling is prevented between sources and detectors. Finally, we comment on potential implications of this approach for dealing with infra-red divergences.