Modelling a Particle Detector in Field Theory

TL;DR

This paper models a particle detector within field theory, emphasizing the stability of the ground state in realistic detectors and deriving an effective model that aligns with physical expectations, contrasting with traditional Unruh-DeWitt detectors.

Contribution

It introduces a realistic detector model based on stable bound states in field theory, challenging the transient excitation behavior of standard models.

Findings

Stable bound states correspond to detector energy levels.

Dressed particle formalism confirms energy eigenstates.

Effective detector model matches physical stability expectations.

Abstract

Particle detector models allow to give an operational definition to the particle content of a given quantum state of a field theory. The commonly adopted Unruh-DeWitt type of detector is known to undergo temporary transitions to excited states even when at rest and in the Minkowski vacuum. We argue that real detectors do not feature this property, as the configuration "detector in its ground state + vacuum of the field" is generally a stable bound state of the underlying fundamental theory (e.g. the ground state-hydrogen atom in a suitable QED with electrons and protons) in the non-accelerated case. As a concrete example, we study a local relativistic field theory where a stable particle can capture a light quantum and form a quasi-stable state. As expected, to such a stable particle correspond energy eigenstates of the full theory, as is shown explicitly by using a dressed particle formalism at first order in perturbation theory. We derive an effective model of detector (at rest) where the stable particle and the quasi-stable configurations correspond to the two internal levels, "ground" and "excited", of the detector.