Eliashberg theory is a theory of superconductivity that describes the role of phonons in providing the attractive interaction between two electrons. Phonon dynamics are taken into account, thus giving rise to retardation effects that impact the electrons, in the form of a frequency-dependent electron self-energy. In the superconducting state, this means that the order parameter, generally considered to be a static quantity in the Bardeen-Cooper-Schrieffer (BCS) theory, also becomes frequency-dependent. Here we review the finite temperature formulation of Eliashberg theory, both on the imaginary and real frequency axis, and briefly display some examples of the consequences of a dynamical, as opposed to static, interaction. Along the way we point out where further work is required, concerning the validity of some of the assumptions used.

中文翻译：

---

Eliashberg 理论：简短回顾

Eliashberg 理论是一种超导理论，它描述了声子在提供两个电子之间的吸引力相互作用方面的作用。声子动力学被考虑在内，从而以依赖于频率的电子自能的形式产生影响电子的延迟效应。在超导状态下，这意味着在 Bardeen-Cooper-Schrieffer (BCS) 理论中通常被认为是静态量的阶次参数也变得与频率相关。在这里，我们回顾了 Eliashberg 理论在虚频率轴和实频率轴上的有限温度公式，并简要展示了一些动态相互作用后果的例子，而不是静态相互作用。在此过程中，我们指出需要进一步工作的地方，涉及使用的一些假设的有效性。