# Impact of relativity on particle localizability and ground state entanglement

## TL;DR

This paper investigates how relativistic effects influence particle localizability and ground state entanglement, revealing persistent issues even in the non-relativistic limit and exploring the nature of the Unruh effect.

## Contribution

It provides a detailed analysis of localizability problems in relativistic quantum field theory and examines the fate of entanglement and the Unruh effect in the non-relativistic approximation.

## Key findings

- Localizability issues persist beyond the Schrödinger regime.
- Ground state entanglement remains significant in the non-relativistic limit.
- The Unruh effect's temperature vanishes as the speed of light approaches infinity.

## Abstract

Can a relativistic quantum field theory be consistently described as a theory of localizable particles? There are many known issues with such a description, indicating an answer in the negative. In this paper, we examine these obstructions by tracing how they (partially) subside in passing to an approximation of ordinary quantum mechanics in the non-relativistic regime. We undertake a recovery of the characteristic features of non-relativistic quantum mechanics beyond simply the Schr\"odinger equation. We find that once this is achieved, there are persisting issues in the localizability of particle states. A major focus is on the lingering discrepancy between two different localization schemes in quantum field theory. The non-relativistic approximation of the quantum field theory is achieved by introducing an ultraviolet cutoff set by the Compton scale. The other main undertaking of this paper is to quantify the fate of ground state entanglement and the Unruh effect in the non-relativistic regime. Observing that the Unruh temperature vanishes in the naive limit as the speed of light is taken to infinity motivates the question: is the Unruh effect relativistic? It happens that this is closely related to the former issues, as ground state entanglement causes obstructions to localizability through the Reeh-Schlieder theorem.