Non-perturbative measurements of two-point functions in quantum field theory

TL;DR

This paper introduces a non-perturbative method using a lattice of particle detectors to directly measure the two-point function of a quantum field in spacetime, emphasizing operational state definitions.

Contribution

It develops a novel detector-based protocol to access quantum field two-point functions non-perturbatively, accounting for finite-size effects through multipole expansion.

Findings

The method accurately encodes the two-point function in detector correlations.

Finite-sized interaction regions cause measurable discrepancies.

The protocol provides an operational way to define quantum states in QFT.

Abstract

We present a non-perturbative method through which local probes can access the two-point function of a quantum field within a region of spacetime. By considering a lattice of gapless particle detectors, we identified the probe observables that encode the field's two-point function. We quantify the discrepancies introduced by physical finite-sized interaction regions by performing a spacetime multipole expansion of the smeared two-point function. Our protocol expresses the two-point function entirely in terms of measurable detectors correlations, providing an operational notion of states in QFT.