A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect

TL;DR

This paper introduces a path integral approach to the Unruh-DeWitt particle detector model, enabling calculations in various spacetimes and trajectories, and connects gauge invariance with nonlocal operators as probes of quantum fields.

Contribution

The paper formulates the UDW detector in the path integral formalism, recovering known results and proposing a gauge-invariant model linked to Wilson line derivatives.

Findings

Path integral formulation of UDW detector in arbitrary spacetimes

Representation of transition probabilities via Feynman diagrams

Proposal of a gauge-invariant detector model related to Wilson lines

Abstract

Particle detectors are an ubiquitous tool for probing quantum fields in the context of relativistic quantum information (RQI). We formulate the Unruh-DeWitt (UDW) particle detector model in terms of the path integral formalism. The formulation is able to recover the results of the model in general globally hyperbolic spacetimes and for arbitrary detector trajectories. Integrating out the detector's degrees of freedom yields a line defect that allows one to express the transition probability in terms of Feynman diagrams. Inspired by the light-matter interaction, we propose a gauge invariant detector model whose associated line defect is related to the derivative of a Wilson line. This is another instance where nonlocal operators in gauge theories can be interpreted as physical probes for quantum fields.