Bounds on negative energy densities in flat spacetime

C J Fewster; S P Eveson

doi:10.1103/PhysRevD.58.084010

Bounds on negative energy densities in flat spacetime

C J Fewster, S P Eveson

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We generalize results of Ford and Roman which place lower bounds-known as quantum inequalities-on the renormalized energy density of a quantum held 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 greater than or equal to 2) for the free real scalar field of mass m greater than or equal to 0. We discuss various features of our bounds in 2 and 4 dimensions. In particular, for massless field theory in two-dimensional Minkowski space, we show that our quantum inequality is weaker than Flanagan's optimal bound by a factor of [S0556-2821(98)03318-9].

Original language	English
Article number	084010
Pages (from-to)	-
Number of pages	6
Journal	Physical Review D
Volume	5808
Issue number	8
DOIs	https://doi.org/10.1103/PhysRevD.58.084010
Publication status	Published - 15 Oct 1998

Keywords

QUANTUM INEQUALITIES

Access to Document

10.1103/PhysRevD.58.084010

http://arxiv.org/abs/gr-qc/9805024

Cite this

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title = "Bounds on negative energy densities in flat spacetime",

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AB - We generalize results of Ford and Roman which place lower bounds-known as quantum inequalities-on the renormalized energy density of a quantum held 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 greater than or equal to 2) for the free real scalar field of mass m greater than or equal to 0. We discuss various features of our bounds in 2 and 4 dimensions. In particular, for massless field theory in two-dimensional Minkowski space, we show that our quantum inequality is weaker than Flanagan's optimal bound by a factor of [S0556-2821(98)03318-9].

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