标题： 绝热正则化用于有质量和无质量的自旋-$1$场 显示英文标题

标题： Adiabatic regularization for massive and massless spin-$1$ fields

摘要： 绝热正则化方法可能是 FLRW 宇宙学中最直接且直观的重整化方案。该方法要求从非零质量开始，但可以通过在计算结束时取零质量极限来研究无质量理论。然而，对于自旋-$1$，这个极限会改变自由度的数量，因此不能直接进行。在这项工作中，我们展示了一种直接的方法，即从具有物理自由度的有质量 Proca 场的经典量子化开始。我们给出了构造的细节，并表明在零质量极限下，Proca 场的重整化能动张量与最小耦合标量场的密切相关。为了完整性和教学目的，我们还简要介绍了标量场的绝热方法。比较了动量空间中绝热减法的构建与 BPHZ 方法用于重整化费曼圈积分的构建。 显示英文摘要

摘要： The adiabatic regularization method is likely the most direct and intuitive renormalization scheme for FLRW cosmologies. The method requires one to start with a nonvanishing mass, but massless theories can be studied by taking the massless limit at the end of the calculations. For spin-$1$, however, this limit changes the number of degrees of freedom, so it cannot be performed directly. In this work, we show a direct approach that begins with the canonical quantization of the physical degrees of freedom of a massive Proca field. We give the details of the construction and show that, in the massless limit, the renormalized stress-energy tensor of the Proca field is closely related to that of a minimally coupled scalar field. For completeness and pedagogical purposes, we also include a brief orientation to the adiabatic method for scalar fields. The construction of the adiabatic subtractions in momentum space is compared with that of the BPHZ method for renormalizing Feynman loop integrals.