X iv : g r - qc / 9 80 50 24 v 2 8 J ul 1 99 8 Bounds on negative energy densities in flat spacetime

We generalise results of Ford and Roman which place lower bounds – known as quantum inequalities – on the renormalised energy density of a quantum field averaged against a choice of sampling function. Ford and Roman derived their results for a specific non-compactly supported sampling function; here we use a different argument to obtain quantum inequalities for a class of smooth, even and non-negative sampling functions which are either compactly supported or decay rapidly at infinity. Our results hold in d-dimensional Minkowski space (d ≥ 2) for the free real scalar field of mass m ≥ 0. We discuss various features of our bounds in 2 and 4 dimensions. In particular, for massless field theory in 2-dimensional Minkowski space, we show that our quantum inequality is weaker than Flanagan's optimal bound by a factor of 3 2 .