Bounds on negative energy densities in flat spacetime

Details Bounds on negative energy densities in flat spacetime Bounds on negative energy densities in flat spacetime

1998-05-07

arxiv.org/abs/gr-qc/9805024v2

Phys.Rev.D58:084010,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

REVTeX, 13 pages and 2 figures. Minor typos corrected, one reference added

Scientific paper

10.1103/PhysRevD.58.084010

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 ($d\ge 2$) for the free real scalar field of mass $m\ge 0$. 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.

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