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Abstract
Quantum energy inequalities (QEIs) express restrictions on the extent to which weighted averages of the renormalized energy density can take negative expectation values within a quantum field theory. Here we derive, for the first time, QEIs for the effective energy density (EED) for the quantized nonminimally coupled massive scalar field. The EED is the quantity required to be nonnegative in the strong energy condition (SEC), which is used as a hypothesis of the Hawking singularity theorem. Thus establishing such quantum strong energy inequalities (QSEIs) is a first step towards a singularity theorem for matter described by quantum field theory.
More specifically, we derive difference QSEIs, in which the local average of the EED is normalordered relative to a reference state, and averaging occurs over both timelike geodesics and spacetime volumes. The resulting QSEIs turn out to depend on the state of interest. We analyse the statedependence of these bounds in Minkowski spacetime for thermal (KMS) states, and show that the lower bounds grow more slowly in magnitude than the EED itself as the temperature increases. The lower bounds are therefore of lower energetic order than the EED, and qualify as nontrivial statedependent QEIs.
More specifically, we derive difference QSEIs, in which the local average of the EED is normalordered relative to a reference state, and averaging occurs over both timelike geodesics and spacetime volumes. The resulting QSEIs turn out to depend on the state of interest. We analyse the statedependence of these bounds in Minkowski spacetime for thermal (KMS) states, and show that the lower bounds grow more slowly in magnitude than the EED itself as the temperature increases. The lower bounds are therefore of lower energetic order than the EED, and qualify as nontrivial statedependent QEIs.
Original language  English 

Article number  045001 
Number of pages  17 
Journal  Physical Review D 
Volume  99 
DOIs  
Publication status  Published  4 Feb 2019 
Bibliographical note
© 2019 American Physical Society. This is an authorproduced version of the published paper. Uploaded in accordance with the publisher’s selfarchiving policy. Further copying may not be permitted; contact the publisher for details.Projects
 1 Finished

QuEST: Quantum Energy Conditions and Singularity Theorems
1/09/17 → 31/08/19
Project: Research project (funded) › Research