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Mass dependence of quantum energy inequality bounds

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Publication details

JournalJournal of Mathematical Physics
DatePublished - Sep 2007
Issue number9
Number of pages13
Pages (from-to)093506:1-13
Original languageEnglish


In a recent paper [C. J. Fewster and M. J. Pfenning, J. Math. Phys. 47, 082303 (2006)], quantum energy inequalities were used to place simple geometrical bounds on the energy densities of quantum fields in Minkowskian space-time regions. Here, we refine this analysis for massive fields, obtaining more stringent bounds which decay exponentially in the mass. At the technical level, this involves the determination of the asymptotic behavior of the lowest eigenvalue of a family of polyharmonic differential equations, a result which may be of independent interest. We compare our resulting bounds with the known energy density of the ground state on a cylinder space-time. In addition, we generalize some of our technical results to general L-p spaces and draw comparisons with a similar result in the literature. (c) 2007 American Institute of Physics.

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