In this review are summarized about 20 years of theoretical research with applications in the field of many-body physics for strongly correlated fermions with Rowe’s equation of motion (R-EOM) method and extended RPA equations. One major goal is to set up, via EOM, RPA equations with a correlated ground state. Since the correlations depend on the RPA amplitudes, it follows that RPA becomes a selfconsistency problem which is called Self-Consistent RPA (SCRPA). This then also improves very much the Pauli principle violated with standard RPA. The method was successfully applied to several non trivial problems, like the nuclear pairing Hamiltonian in the particle–particle channel (pp-RPA) and the Hubbard model of condensed matter. The SCRPA has several nice properites, as for instance, it can be formulated in such a way that all very appreciated qualities of standard RPA as, e.g., appearance of zero (Goldstone) modes in the case of broken symmetries, conservation laws, Ward identities, etc. are maintained. For the Goldstone mode an explicit example of a model case is presented. The formalism has its sound theoretical basis in the fact that an extension of the usual RPA operator has been found which exactly annihilates the Coupled Cluster Doubles (CCD) ground state wave function. This has been a longstanding problem for all RPA practioners from the beginning. There exists a rather simplified version of SCRPA which is the so-called renormalized RPA (r-RPA) where only the correlated occupation numbers are involved in the selfconsistent cycle. Because its numerical solution is rather similar to standard RPA, it has known quite a number of applications, like beta and double beta decays, which are reviewed in this article. In this review also an extended version of second RPA (ERPA)is described. This ERPA maintains all appreciable properties of standard RPA. Several realistic applications for, e.g., the damping of giant resonances are presented. Another important aspect of the extended RPA-theories is that it can be formulated symmetry conserving replacing and eventually improving symmetry (e.g., number) projected mean field approaches. A practical application is given in the review. The EOM formalism allows to treat alpha clustering and alpha particle (quartet) condensation in nuclear matter. This EOM approach succeeded where earlier attempts have failed. It is, for instance, shown how the critical temperature for alpha particle condensation in symmetric and asymmetric nuclear matter can efficiently be calculated.

在这篇综述中，总结了大约 20 年的理论研究以及在多体物理领域的应用，这些研究使用 Rowe 的运动方程 (R-EOM) 方法和扩展的 RPA 方程来研究强相关费米子。一个主要目标是通过 EOM 建立具有相关基态的 RPA 方程。由于相关性取决于 RPA 幅度，因此 RPA 成为自洽问题，称为自洽 RPA (SCRPA)。这也极大地改进了标准 RPA 违反的泡利原则。该方法已成功应用于几个重要问题，如粒子-粒子通道中的核配对哈密顿量 (pp-RPA) 和凝聚态的哈伯德模型。SCRPA 有几个不错的特性，例如，它可以用这样的方式来表述，即标准 RPA 的所有非常受欢迎的品质，例如，在对称性、守恒定律、沃德恒等式等情况下出现零（戈德斯通）模式。对于 Goldstone 模式，给出了一个模型案例的明确示例。形式主义有其可靠的理论基础，因为已经发现了通常的 RPA 算子的扩展，它恰好消除了耦合簇双 (CCD) 基态波函数。从一开始，这就是所有 RPA 从业者长期存在的问题。存在一个相当简化的 SCRPA 版本，即所谓的重归一化 RPA（r-RPA），其中只有相关的职业数参与自洽循环。因为它的数值解与标准 RPA 相当相似，它已经知道了相当多的应用，例如 beta 和双 beta 衰减，本文将对其进行回顾。在这篇评论中，还描述了第二个 RPA (ERPA) 的扩展版本。该 ERPA 保留了标准 RPA 的所有显着属性。介绍了几种实际应用，例如，巨型共振的阻尼。扩展 RPA 理论的另一个重要方面是，它可以被公式化为对称守恒替换并最终改进对称（例如，数字）投影平均场方法。评论中给出了一个实际应用。EOM 形式允许处理核物质中的 alpha 聚类和 alpha 粒子（四重奏）凝聚。这种 EOM 方法在早期尝试失败的地方取得了成功。例如，它是