论文标题
狄拉克栅地状态的新定义
A new definition of the Dirac-Fock ground state
论文作者
论文摘要
当无法忽略相对论效应时，dirac-fock（DF）模型取代了量子化学中的Hartree-fock（HF）近似。由于狄拉克操作员没有从下方界定，因此基态的概念在该模型中是有问题的，并且文献中提出了一些定义。我们为DF Energy的基态提供了新的定义，灵感来自Lieb放松的HF变异原理。我们的定义和存在证明比以前在DF上的作品更简单，更自然，但比非依赖主义情况更具技术性。首先需要构建一组在物理上可接受的密度矩阵，以满足某些非线性固定点方程：我们通过引入迭代过程来做到这一点，这是在抽象上下文中描述的。然后，在该集合中发现基态是DF能量的最小化器。
The Dirac-Fock (DF) model replaces the Hartree-Fock (HF) approximation in quantum chemistry when relativistic effects cannot be neglected. Since the Dirac operator is not bounded from below, the notion of ground state is problematic in this model, and several definitions have been proposed in the literature. We give a new definition for the ground state of the DF energy, inspired of Lieb's relaxed variational principle for HF. Our definition and existence proof are simpler and more natural than in previous works on DF, but remains more technical than in the nonrelativistic case. One first needs to construct a set of physically admissible density matrices that satisfy a certain nonlinear fixed-point equation: we do this by introducing an iterative procedure, described in an abstract context. Then the ground state is found as a minimizer of the DF energy on this set.
