Lifshitz围巾
Scarf for Lifshitz
摘要：
研究了真空以及具有分段光滑不均匀性的色散和耗散介质的极化问题，目的是澄清发散电磁应力-能量张量的重正化问题。首先，应力张量计算与伦敦力的Lifshitz方法在非延迟的限制，扣除后的领先的自由空间紫外线发散仍然保留与分段之间的不均匀性的尖锐边界的存在相关的发散。我们称这些贡献为有限的，因为它们成为重整化后，尖锐的接口被替换为根据空间坐标的平滑函数变化的介电常数。此外，这样一个平滑的接口表现出新的subleading紫外发散，出现由于其内部结构。为了系统地处理非均匀介质的极化，阿达玛展开被应用到挑选出有限和subleading贡献，并明确地证明不完全重整化的Lifshitz理论。上述方法还使我们能够揭示表面张力的本质，这被证明是纯粹的量子力学。推导出的表面张力理论及其对实际电介质的计算结果与实验数据进行了比较。虽然锐界面极限恢复了电场的经典边界条件，并揭示了文献中先前指出的锐界面公式中重整化应力的明显局部发散的起源，表面张力问题被证明是一个特殊的极限类型，因为尖锐的界面公式失去了关于界面内部结构的信息，因此不能解释表面张力的起源。
英文摘要：
Polarization of a vacuum as well as of dispersive and dissipative dielectric media with piece-wise and smooth inhomogeneities is studied with the goal to clarify the question of renormalizability of diverging electromagnetic stress-energy tensor. First, the stress tensor is computed with the Lifshitz approach to London forces in the non-retarded limit, which after the substraction of the leading free space ultraviolet divergencies still retains the divergencies associated with the presence of sharp boundaries between piece-wise inhomogeneities. We call these contributions finite because they become renormalized after a sharp interface is replaced with a dielectric permittivity changing according to a smooth function of spatial coordinates. In addition, such a smoothed out interface exhibits new subleading ultraviolet divergencies that appear due to its internal structure. To systematically deal with the polarization of inhomogeneous media, the Hadamard expansion is applied to single out both finite and subleading contributions and to unequivocally demonstrate incomplete renormalizability of the Lifshitz theory. The above approach also allows us to reveal the nature of surface tension, which proves to be purely quantum mechanical. The deduced theory of surface tension and its calculations for real dielectric media are favorably compared to the available experimental data. While the sharp interface limit recovers the classical boundary conditions for the electric field and uncovers the origin of the apparent local divergencies of the renormalized stresses in the sharp interface formulation previously pointed out in the literature, the problem of surface tension proves to be of a distinguished limit type because the sharp interface formulation loses the information about the internal structure of an interface and hence cannot explain the origin of surface tension.
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