真空能量的质量依赖性
Mass Dependence of Vacuum Energy
摘要：
本文证明了在静态外条件下量子场的正则化真空能量（或能量密度）满足关于质量和“时间”（紫外截止参数）这两个变量的偏微分方程。求解该方程，以提供正质量下的正则化能量（更准确地说，圆柱核）在零质量下的积分表达式。或者，对于固定的正质量，正则化能量的短时渐近中的所有系数都可以从第一个非平凡系数（重整化真空能量）递归地获得。
英文摘要：
The regularized vacuum energy (or energy density) of a quantum field subjected to static external conditions is shown to satisfy a certain partial differential equation with respect to two variables, the mass and the "time" (ultraviolet cutoff parameter). The equation is solved to provide integral expressions for the regularized energy (more precisely, the cylinder kernel) at positive mass in terms of that for zero mass. Alternatively, for fixed positive mass all coefficients in the short-time asymptotics of the regularized energy can be obtained recursively from the first nontrivial coefficient, which is the renormalized vacuum energy.
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。
