Bounds on negative energy densities in flat spacetime

C. J. Fewster and S. P. Eveson
Phys. Rev. D 58, 084010 – Published 1 September 1998
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Abstract

We generalize results of Ford and Roman which place lower bounds—known as quantum inequalities—on the renormalized 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 two-dimensional Minkowski space, we show that our quantum inequality is weaker than Flanagan’s optimal bound by a factor of 32.

  • Received 8 May 1998

DOI:https://doi.org/10.1103/PhysRevD.58.084010

©1998 American Physical Society

Authors & Affiliations

C. J. Fewster* and S. P. Eveson

  • Department of Mathematics, University of York, Heslington, York YO10 5DD, United Kingdom

  • *Electronic address: cjf3@york.ac.uk
  • Electronic address: spe1@york.ac.uk

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Issue

Vol. 58, Iss. 8 — 15 October 1998

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