Schwinger Pair Production and the Extended Uncertainty Principle: Can Heuristic Derivations Be Trusted?

TL;DR

This paper examines whether heuristic derivations of Schwinger pair production rates, based on the extended uncertainty principle (EUP), are reliable, especially in curved spacetimes like anti-de Sitter and de Sitter.

Contribution

The study demonstrates that EUP can correctly predict Schwinger pair production rates in curved spacetimes, clarifying the role of correction sign and questioning the trustworthiness of heuristic methods.

Findings

EUP yields correct pair production rates in anti-de Sitter spacetime.

The sign of the EUP correction term is crucial for accuracy.

Highlights inconsistencies in previous EUP literature.

Abstract

The rate of Schwinger pair production due to an external electric field can be derived heuristically from the uncertainty principle. In the presence of a cosmological constant, it has been argued in the literature that the uncertainty principle receives a correction due to the background curvature, which is known as the "extended uncertainty principle" (EUP). We show that EUP does indeed lead to the correct result for Schwinger pair production rate in anti-de Sitter spacetime (the case for de Sitter spacetime is similar), provided that the EUP correction term is negative (positive for the de Sitter case). We compare the results with previous works in the EUP literature, which are not all consistent. Our result further highlights an important issue in the literature of generalizations of the uncertainty principle: how much can heuristic derivations be trusted?