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. 
L.H. Ford and Thomas A. Roman