Mass Dependence of Quantum Energy Inequality Bounds

Details Mass Dependence of Quantum Energy Inequality Bounds Mass Dependence of Quantum Energy Inequality Bounds

2007-02-21

arxiv.org/abs/math-ph/0702074v1

J.Math.Phys.48:093506,2007

Physics

Mathematical Physics

15pp LaTeX2e

Scientific paper

10.1063/1.2779137

In a recent paper [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 spacetime 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 behaviour 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 spacetime. In addition, we generalise some of our technical results to general $L^p$-spaces and draw comparisons with a similar result in the literature.

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