I present a review on non relativistic effective energy--density functionals (EDFs). An introductory part is dedicated to traditional phenomenological functionals employed for mean--field--type applications and to several extensions and implementations that have been suggested over the years to generalize such functionals, up to the most recent ideas. The heart of this review is then focused on density functionals designed for beyond--mean--field models. Examples of these studies are discussed. Starting from these investigations, some illustrations of {\it{ab--initio}}--based or {\it{ab--initio}}--inspired functionals are provided. Constructing functionals by building bridges with {\it{ab--initio}} models represents an extremely challenging and timely objective. This will eventually reduce/eliminate the empirical character of EDFs and link them with the underlying theory of QCD. Conclusions are presented in the last part of the review.

中文翻译：

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超出平均场的有效密度泛函

我对非相对论有效能量密度泛函 (EDF) 进行了综述。介绍性部分专门介绍用于平均场类型应用程序的传统现象学泛函，以及多年来提出的几种扩展和实现，以概括这些泛函，直到最近的想法。此评论的核心然后集中在为超平均场模型设计的密度泛函。讨论了这些研究的例子。从这些调查开始，提供了一些基于 {\it{ab--initio}}--或 {\it{ab--initio}}--启发的泛函的说明。通过使用 {\it{ab--initio}} 模型构建桥梁来构建泛函是一个极具挑战性和及时性的目标。这最终将减少/消除 EDF 的经验特征，并将它们与 QCD 的基本理论联系起来。结论在审查的最后部分提出。