Bounds on negative energy densities in flat spacetime
arXiv:gr-qc/9805024 · doi:10.1103/PhysRevD.58.084010
Abstract
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 -dimensional Minkowski space () for the free real scalar field of mass . 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.
REVTeX, 13 pages and 2 figures. Minor typos corrected, one reference added
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