Towards local and compositional measurements in quantum field theory

TL;DR

This paper develops a framework for localized and compositional measurements in quantum field theory, integrating the positive formalism with path integral techniques to ensure locality, positivity, and consistency in measurement processes.

Contribution

It introduces a modulus-square construction for measurement formalization and a renormalization scheme for quadratic observables that preserves compositionality.

Findings

The measurement scheme satisfies positivity, locality, and compositionality.

The renormalization scheme for quadratic observables maintains these properties.

Measurements are confirmed to be localized in spacetime regions where observables have support.

Abstract

A universal framework for the joint measurement of multiple localized observables in quantum field theory satisfying spacetime locality and compositionality is still lacking. We present an approach to the problem that is based on the one hand on the positive formalism, an axiomatic framework, where it is clear from the outset that we satisfy locality and compositionality, while also having a consistent probabilistic interpretation. On the other hand, the approach is based on standard tools from quantum field theory, in particular the path integral and the Schwinger-Keldysh formalism. After an overview of the conceptual foundations we introduce the modulus-square construction as a formalization of the measurement process for an important class of observables including quadratic observables. We show that this construction has many of the desired properties, including positivity, locality, single measurement recovery and compositionality. We introduce a renormalization scheme for the measurement of quadratic observables that also satisfies compositionality, in contrast to previous renormalization schemes. We discuss relativistic causality, confirming that measurements in our scheme are indeed localized in the spacetime regions where the underlying observables have support.