The Unruh-deWitt Detector and the Vacuum in the General Boundary formalism

TL;DR

This paper explores how the vacuum state of a quantum scalar field can be determined in the general boundary formalism by analyzing the response of an Unruh-DeWitt detector, especially in the presence of evanescent modes near boundaries.

Contribution

It introduces a method to select the vacuum state in the GBF using detector responses, emphasizing the influence of external physical conditions.

Findings

The vacuum state depends on external physical situations.

Evanescent modes significantly affect the detector response.

Vacuum determination requires considering the entire physical context.

Abstract

We discuss how to formulate a condition for choosing the vacuum state of a quantum scalar field on a timelike hyperplane in the general boundary formulation (GBF) using the coupling to an Unruh-DeWitt detector. We explicitly study the response of an Unruh-DeWitt detector for evanescent modes which occur naturally in quantum field theory in the presence of the equivalent of a dielectric boundary. We find that the physically correct vacuum state has to depend on the physical situation outside of the boundaries of the spacetime region considered. Thus it cannot be determined by general principles pertaining only to a subset of spacetime.