Probabilities and signalling in quantum field theory

TL;DR

This paper introduces a probability-based approach in quantum field theory that uses expectation values of nested commutators and anti-commutators, clarifying causality and enabling analysis of source-detector models.

Contribution

It develops a novel method for computing probabilities directly in quantum field theory, emphasizing the role of retarded propagators and providing new tools for causality analysis.

Findings

Derived expressions for vacuum expectation values of nested commutators and anti-commutators.

Demonstrated how the formalism prevents faster-than-light signalling.

Applied the approach to the Fermi two-atom problem.

Abstract

We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can be written in terms of expectation values of nested commutators and anti-commutators. We present results that help in the evaluation of these, including an expression for the vacuum expectation values of general nestings of commutators and anti-commutators in scalar field theory. This approach allows one to see clearly how faster-than-light signalling is prevented, because it leads to a diagrammatic expansion in which the retarded propagator plays a prominent role. We illustrate the formalism using the simple case of the much-studied Fermi two-atom problem.