Particle detector models from path integrals of localized quantum fields

TL;DR

This paper establishes a connection between localized quantum field theories and particle detector models using path integrals, providing a systematic way to derive corrections and extend the theoretical framework in relativistic quantum information.

Contribution

It demonstrates that the dynamics of localized quantum fields can be exactly modeled by Unruh-DeWitt detectors at leading order, with a systematic method for higher-order corrections via path integrals.

Findings

Exact equivalence between localized quantum fields and UDW detectors at leading order

Closed-form expression for higher-order corrections in perturbation theory

Extends the bridge between detector models and field theory frameworks

Abstract

Using the Schwinger-Keldysh path integral, we draw a connection between localized quantum field theories and more commonly used models of local probes in Relativistic Quantum Information (RQI). By integrating over and then tracing out the inaccessible modes of the localized field being used as a probe, we show that, at leading order in perturbation theory, the dynamics of any finite number of modes of the probe field is exactly that of a finite number of harmonic-oscillator Unruh-DeWitt (UDW) detectors. The equivalence is valid for a rather general class of input states of the probe-target field system, as well as for any arbitrary number of modes included as detectors. The path integral also provides a closed-form expression which gives us a systematic way of obtaining the corrections to the UDW model at higher orders in perturbation theory due to the existence of the additional modes that have been traced out. This approach vindicates and extends a recently proposed bridge between detector-based and field-theory-based measurement frameworks for quantum field theory [T. R. Perche et al., Particle detectors from localized quantum field theories, Phys. Rev. D 109, 045013 (2024)], and also points to potential connections between particle detector models in RQI and other areas of physics where path integral methods are more commonplace -- in particular, the Wilsonian approach to the renormalization group and effective field theories.