One always looks for a simplified technique and desirable formalism, to solve the Hamiltonian, and to find the wave function, energy, etc, of a many-body system. The lowest order constrained variational ($LOCV$) method is designed such that, to fulfill the above requirements. The $LOCV$ formalism is based on the first two, i.e., lowest order, terms of the cluster expansion theory with the $Jastrow$ correlation functions as its inputs. A constraint is imposed for the normalization of the total correlated two-body wave functions, which also forces the cluster expansion series to converge very rapidly. The variation of $Jastrow$ correlation functions subjected to the above normalization constraint, leads to the sets of Euler–Lagrange equations, which generates the required correlation functions. In order to satisfy the normalization constraint exactly, one has to define the long-range behaviors, for the two-body correlation functions, i.e., the Pauli function. The primary developments of $LOCV$ formalism, and some of its applications were reviewed in this journal by Max Irvine in 1981. Since then (1981–2022), the various extensions and applications of the $LOCV$ method are reported through the several published articles (nearly 180 items), which are the subjects of this review. (i) It is shown that the $LOCV$ results can be, as good as, the various more complicated and computer time-consuming techniques, such as the Fermi $hypernetted$ chain ($FHNC$), Monte Carlo ($MC$), G-matrix, etc, calculations. (ii) Moreover, the $LOCV$ method is further developed to deal with the more sophisticated interactions, such as the $AV18$, $UV14$, etc, nucleon–nucleon potentials, using the state-dependent correlation functions, and applicable to perform the finite temperature calculations. The extended $LOCV$ ($ELOCV$) method is also introduced for the state-independent media. (iii) Its convergence is tested through the calculation of three-body cluster series, with the state-dependent correlation functions, which confirm the old (1979) state-averaged predictions. Finally, its application to the $nucleonic$ and $\beta -$stable matter with and without the three-body force, the finite nuclei, the liquid helium 3, the neutron star, etc are performed and compared with the other many-body techniques. As we stated before, in this review, we definitely go through the most of above items.

人们总是在寻找一种简化的技术和理想的形式主义来解决哈密顿量，并找到多体系统的波函​​数、能量等。最低阶约束变分 ($\mathrm{大号}欧CV$) 方法旨在满足上述要求。这$\mathrm{大号}欧CV$形式主义是基于前两个，即最低阶，聚类扩展理论的术语$杰A秒吨row$相关函数作为其输入。对总相关二体波函数的归一化施加了约束，这也迫使簇扩展级数非常迅速地收敛。的变化_$杰A秒吨row$受上述归一化约束的相关函数导致生成所需相关函数的欧拉-拉格朗日方程组。为了准确满足归一化约束，必须定义双体相关函数的长程行为，即泡利函数。的主要发展$\mathrm{大号}欧CV$Max Irvine 于 1981 年在本期刊中评论了形式主义及其一些应用。从那时起（1981-2022），形式主义的各种扩展和应用$\mathrm{大号}欧CV$方法通过几篇发表的文章（近 180 篇）进行了报道，这些文章是本综述的主题。(i) 结果表明$\mathrm{大号}欧CV$结果可能与各种更复杂且耗时的计算机技术一样好，例如费米$H是p\mathrm{电子}rn\mathrm{电子}吨吨\mathrm{电子}d$链 （$FH否C$）， 蒙特卡洛 （$米C$)、G矩阵等计算。(ii) 此外，$\mathrm{大号}欧CV$方法被进一步开发以处理更复杂的交互，例如$AV18$,$üV14$等，核子-核子势，使用状态相关的相关函数，适用于执行有限温度计算。扩展的$\mathrm{大号}欧CV$ ($乙\mathrm{大号}欧CV$) 方法也被引入到与状态无关的媒体中。(iii) 它的收敛性是通过三体簇系列的计算来检验的，具有状态相关的相关函数，这证实了旧的（1979 年）状态平均预测。最后，它的应用$n你C升\mathrm{电子}on我C$和$\beta -$进行了具有和不具有三体力的稳定物质、有限核、液氦 3 、中子星等，并与其他多体技术进行了比较。正如我们之前所说，在这次审查中，我们肯定会经历上述大部分项目。