The many-body problem cannot in general be solved exactly, and one of the most prominent approximations is to build perturbation expansions. A huge variety of expansions are possible, which differ by the quantity to be expanded, the expansion variable, the starting point, and ideas of how to re-sum or terminate the series. Although much has been discussed and much has been done, some choices were made for historical reasons, in particular, limited computation or storage capacities. The present work aims to examine the justification for different choices made in different contexts, by comparing the components of functionals based on Green’s functions on the one side, and on the charge density on the other side. Of particular interest will be the question of how to build an optimal starting point for the approximation of non-local quantities, making use of near- or far-sightedness, and daring to consider models beyond the homogeneous electron gas. This will include the use of connector approximations. We will also discuss why it is a good idea to build functionals of the density.

中文翻译：

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建立密度函数或格林函数的函数的策略：我们可以学到什么？

一般而言，多体问题无法完全解决，最突出的近似之一是建立扰动展开。可能有各种各样的扩展，这些扩展因要扩展的数量，扩展变量，起点以及如何重新求和或终止序列的思路而异。尽管已经进行了很多讨论并做了很多工作，但是由于历史原因做出了一些选择，特别是有限的计算或存储容量。通过比较一方面基于格林函数的功能组件和另一方面基于电荷密度的功能组件，本工作旨在检验在不同情况下做出不同选择的合理性。特别令人感兴趣的问题是如何为非本地数量的近似建立最佳起点，利用近视或远视，并敢于考虑均质电子气以外的模型。这将包括使用连接器近似值。我们还将讨论为什么建立密度函数是一个好主意。