论文标题
在有限密度计算中以边界项来增强残留定理
Augmenting the residue theorem with boundary terms in finite-density calculations
论文作者
论文摘要
在零温度和有限的化学势下，$ d $维循环积分具有具有复杂值的集成在虚构时间形式主义产量结果中取决于整合顺序的结果。即使使用最简单的一环尺寸正规化积分，我们也会观察到这一点。通过评估暂时$ \ mathrm {d} p_0 $积分$积分$积分的空间$ \ mathrm {d}^{d} p $积分来计算此类积分，从而与在小但不变温度下获得的结果一致。首先通过将残基定理应用于集成来计算时间积分会产生不同的答案。一般复杂的繁殖者也是如此。在这项工作中，我们旨在了解这种差异背后的理论背景，以便充分实现应用程序中残留微积分的强大技术。我们将差异投入了与Dirac Deltas相关的衍生术语的形式，并进一步证明了差异是如何源自费米 - 迪拉克职业函数的零温度极限，被视为复杂值函数。我们还讨论了向非全能力量提出的传播器的概括。
At zero temperature and finite chemical potential, $d$-dimensional loop integrals with complex-valued integrands in the imaginary-time formalism yield results dependent on the integration order. We observe this even with the simplest one-loop dimensionally regularized integrals. Computing such integrals by evaluating the spatial $\mathrm{d}^{d} p$ integral before the temporal $\mathrm{d} p_0$ integral yields results consistent with those obtained at small but nonvanishing temperatures. Computing the temporal integral first by applying the residue theorem to the integrand yields a different answer. The same holds for general complexified propagators. In this work we aim to understand the theoretical background behind this difference, in order to fully enable the powerful techniques of residue calculus in applications. We cast the difference into the form of a derivative term related to Dirac deltas, and further demonstrate how the difference originates from the zero-temperature limit of the Fermi-Dirac occupation functions treated as complex-valued functions. We also discuss a generalization to propagators raised to non-integer powers.
