2007/02/28 by Christopher J. Fewster, Calvin J. Smith · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #gr-qc
paper · pdf · doi:10.1007/s00023-008-0361-0
published as AnnalesHenriPoincare9:425-455,2008 · 31 pages. Corrections and clarifications added. Final version to appear in Ann. H. Poincare
arxiv created 2007/12/20 · openalex publication_date 2008/04/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantum Energy Inequalities (QEIs) are results which limit the extent to which the smeared renormalised energy density of the quantum field can be negative, when averaged along a timelike curve or over a more general timelike submanifold in spacetime. On globally hyperbolic spacetimes the minimally-coupled massive quantum Klein--Gordon field is known to obey a `difference' QEI that depends on a reference state chosen arbitrarily from the class of Hadamard states. In many spacetimes of interest this bound cannot be evaluated explicitly. In this paper we obtain the first `absolute' QEI for the minimally-coupled massive quantum Klein--Gordon field on four dimensional globally hyperbolic spacetimes; that is, a bound which depends only on the local geometry. The argument is an adaptation of that used to prove the difference QEI and utilises the Sobolev wave-front set to give a complete characterisation of the singularities of the Hadamard series. Moreover, the bound is explicit and can be formulated covariantly under additional (general) conditions. We also generalise our results to incorporate adiabatic states.