Restrictions on Negative Energy Density in Flat Spacetime

TL;DR

This paper simplifies the derivation of quantum inequalities that limit negative energy density in flat spacetime, extending results to electromagnetic and massive scalar fields across different dimensions.

Contribution

It introduces a simpler method for deriving bounds on negative energy density, applicable to various fields and spacetime dimensions, improving upon previous complex analyses.

Findings

Derived quantum inequality bounds for electromagnetic fields.

Extended bounds to massive scalar fields in 2D and 4D.

Provided a more straightforward derivation method.

Abstract

In a previous paper, a bound on the negative energy density seen by an arbitrary inertial observer was derived for the free massless, quantized scalar field in four-dimensional Minkowski spacetime. This constraint has the form of an uncertainty principle-type limitation on the magnitude and duration of the negative energy density. That result was obtained after a somewhat complicated analysis. The goal of the current paper is to present a much simpler method for obtaining such constraints. Similar ``quantum inequality'' bounds on negative energy density are derived for the electromagnetic field, and for the massive scalar field in both two and four-dimensional Minkowski spacetime.