Detector-based measurements for QFT: two issues and an AQFT proposal

TL;DR

This paper identifies issues in a detector-based measurement scheme for quantum field theory and proposes a modified approach using non-relativistic detectors to ensure consistent evaluation of n-point functions across causally related regions.

Contribution

It introduces a modified measurement scheme employing non-relativistic detectors to resolve inconsistencies in the original QFT measurement framework.

Findings

Identified discrepancies in the original measurement scheme with contextual field states.

Proposed a modified scheme ensuring consistent n-point function evaluations.

Achieved a more coherent algebraic state update rule in AQFT.

Abstract

We present and investigate two issues within the measurement scheme for QFT presented by J. Polo-G\'omez, L. J. Garay and E. Mart\'in-Mart\'inez in "A detector-based measurement theory for quantum field theory". We point out some discrepancies that arise when the measurement scheme is applied to contextual field states and show that $n$-point function assignments based on local processing regions sometimes lead to inconsistencies. To solve these issues, we modify the measurement scheme to use non-relativistic detectors to induce an update rule for algebraic states in the Haag-Kastler formulation of quantum field theory. In this way, $n$-point functions can be consistently evaluated across any region having a definite causal relation with measurements.