量子能量不等式界的质量依赖性
Mass Dependence of Quantum Energy Inequality Bounds
摘要：
在最近的一篇论文[J. Math. Phys. 47 082303（2006）]中，量子能量不等式被用来对闵可夫斯基时空区域中量子场的能量密度设置简单的几何界限。在这里，我们完善了大规模领域的分析，获得更严格的边界，在质量指数衰减。在技术层面上，这涉及到确定的渐近行为的最低本征值的一个家庭的多谐微分方程，一个结果，这可能是独立的利益。我们比较我们的结果与已知的基态的能量密度的圆柱时空的边界。此外，我们推广我们的一些技术结果一般$L^p$-空间，并绘制与文献中类似的结果进行比较。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
