Restrictions on negative energy density in flat spacetime

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.