Causal measurement in quantum field theory: spacetime

TL;DR

This paper develops a framework for measuring spacetime-localized observables in quantum field theory that respects causality and avoids superluminal signaling, extending previous instantaneous measurement results.

Contribution

It introduces a regularized, spacetime-compositional measurement framework for bosonic quantum fields that ensures relativistic causality and causal transparency.

Findings

Measurements satisfy relativistic causality and avoid superluminal signaling.

Time-extended measurements induce correlations in their causal future.

Framework extends previous instantaneous measurement results.

Abstract

We provide a framework and explicit construction for the regularized measurement of a large class of spacetime-localized observables in bosonic quantum field theory. The measurements fully satisfy relativistic causality and causal transparency, i.e., avoid unphysical superluminal signaling. We show explicitly how the measurement of time-extended observables back-reacts on itself and induces correlations between other measurements in its causal future. Our framework is fully compositional in spacetime and extends previous results on the measurement of instantaneous observables.