How to define the moving frame of the Unruh-DeWitt detector on manifolds

TL;DR

This paper develops a rigorous local differential geometric framework to define the moving frame of the Unruh-DeWitt detector, addressing discrepancies and the relationship between entanglement and geometry.

Contribution

It introduces a method to define the vacuum in a moving frame using vierbeins and exact WKB, resolving the Stokes phenomenon and discrepancies in the Unruh-DeWitt detector analysis.

Findings

Resolved the factor 2 discrepancy in the Unruh-DeWitt detector results.

Established a local, non-perturbative calculation framework using differential geometry.

Linked entanglement phenomena with the geometric structure of spacetime.

Abstract

The physical phenomena seen by an observer are defined for a local inertial system that is subjective to the observer. Such a coordinate system is called a ``moving frame'' because it changes from time to time. However, unlike the Thomas precession, the Unruh-DeWitt detector has been discussed for a fixed frame. We discuss the Unruh-DeWitt detector by defining the vacuum for the moving frame, showing that the problem of the Stokes phenomenon can be solved by using the vierbeins and the exact WKB, to find factor 2 discrepancy from the standard result. Differential geometry is constructed in such a way that local calculations can be performed rigorously. If one expects Markov property, the calculation is expected to be local. The final piece that was missing was a local non-perturbative calculation, which is now complemented by the exact WKB. Our analysis defines a serious problem regarding the relationship between entanglement of the Unruh effect and differential geometry.