Polarization of dispersive and dissipative dielectric media with smoothed-out inhomogeneities is studied with the goal to clarify the question of renormalizability of electromagnetic stress–energy tensor. The stress tensor is computed with the Lifshitz approach to van der Waals forces in the non-retarded limit, which accounts for dominant effects at the distances from the interface shorter than the absorption wavelength. After the substraction of the leading free space ultraviolet divergencies, there still remain two types of divergencies. First, contributions diverging in the sharp interface case become finite once it is smoothed out. Second, new subleading ultraviolet cut-off-dependent contributions appear due to the interface internal structure. The Hadamard expansion, based on the heat kernel method, is applied to systematically single out both finite and subleading contributions and to demonstrate incomplete renormalizability of the Lifshitz theory. The above approach also allows us to reveal the purely quantum mechanical nature of surface tension, which consists of finite cut-off-independent as well as cut-off-dependent contributions. The deduced theory of surface tension and its calculations for real dielectric media are favourably compared to the available experimental data. The problem of surface tension proves to be of a distinguished limit type because the sharp interface formulation loses the critical information about the internal structure of an interface. The general theory offered here is illustrated with an exactly solvable model representing a smooth transition between two different dielectric media, which relies upon a solution of the Schrödinger equation with the Scarf potential.

研究了具有平滑不均匀性的色散和耗散介电介质的极化，目的是澄清电磁应力 - 能量张量的可重整化问题。应力张量是使用 Lifshitz 方法计算的，用于非延迟极限中的范德华力，这解释了与界面距离短于吸收波长的主要影响。减去领先的自由空间紫外发散后，仍然存在两种类型的发散。首先，在尖锐界面情况下发散的贡献一旦被平滑就变得有限。二、新分词由于界面内部结构，出现了依赖于紫外线截止的贡献。应用基于热核方法的 Hadamard 展开来系统地挑选出有限和次主导的贡献，并证明 Lifshitz 理论的不完全重整化性。上述方法还允许我们揭示表面张力的纯量子力学性质，它由与有限截止无关以及与截止相关的贡献组成。表面张力的推导理论及其对实际介电介质的计算与可用的实验数据相比是有利的。表面张力问题被证明是一个显着的极限类型，因为锐界面公式丢失了有关界面内部结构的关键信息。这里提供的一般理论用一个完全可解的模型来说明，该模型代表两种不同介电介质之间的平滑过渡，该模型依赖于具有斯卡夫势的薛定谔方程的解。