2007/02/21 by Simon P. Eveson, Christopher J. Fewster · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math-ph #math.MP
paper · pdf · doi:10.1063/1.2779137
published as J.Math.Phys.48:093506,2007 · 15pp LaTeX2e
arxiv created 2007/02/21 · openalex publication_date 2007/09/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 Lp spaces and draw comparisons with a similar result in the literature.