In this paper, connections are uncovered between the averaged weak (AWEC) and averaged null (ANEC) energy condtions, and quantum inequality restrictions (uncertainty-principle-type inequalities) on negative energy. In two- and four-dimensional Minkowski spacetime, we examine quantized, free massless, minimally coupled scalar fields. In a two-dimensional spatially compactified Minkowski universe, we derive a covariant quantum inequality-type bound on the difference of the expectation values of… CONTINUE READING