The stress-energy tensor of an Unruh-DeWitt detector

TL;DR

This paper develops a covariant model for a finite-size Unruh-DeWitt detector, deriving its stress-energy tensor from a Lagrangian that includes quantum fields, a complex scalar, and a perfect fluid, ensuring physical reasonableness.

Contribution

It introduces a novel covariant Lagrangian framework for modeling a finite-size particle detector and deriving its stress-energy tensor, incorporating localization and energy condition considerations.

Findings

The energy tensor satisfies physical energy conditions.

The model ensures square integrability of detector modes.

The framework is applicable under general conditions.

Abstract

We propose a model for a finite-size particle detector, which allows us to derive its stress-energy tensor. This tensor is obtained from a covariant Lagrangian that describes not only the quantum field that models the detector, $\phi_{\text{d}}$, but also the systems responsible for its localization: a complex scalar field, $\psi_{\text{c}}$, and a perfect fluid. The local interaction between the detector and the complex field ensures the square integrability of the detector modes, while the fluid serves to define the spatial profile of $\psi_{\text{c}}$, localizing it in space. We then demonstrate that, under very general conditions, the resulting energy tensor -- incorporating all components of the system -- is physically reasonable and satisfies the energy conditions.