密度-势映射的结构。第一部分：标准密度泛函理论
The structure of the density-potential mapping. Part I: Standard density-functional theory
AI总结：
本文综述了Hohenberg-Kohn定理在标准密度泛函理论中的真正地位，论证其并非DFT的基础，而是一个更全面数学框架的推论，为构建广义DFT提供指导。
摘要：
密度泛函理论（DFT）的Hohenberg-Kohn定理被广泛认为是仅通过单体粒子密度即可完整刻画电子系统基态的概念基础。本综述的第一部分旨在澄清Hohenberg-Kohn定理在DFT中的地位，第二部分则讨论包含磁场的理论的不同扩展。我们收集证据表明，Hohenberg-Kohn定理与其说是DFT的基础，不如说是一个更全面的数学框架的结果。这些结果在构建广义DFT时尤其有用。
英文摘要：
The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review aims at clarifying the status of the Hohenberg-Kohn theorem within DFT and Part II at different extensions of the theory that include magnetic fields. We collect evidence that the Hohenberg-Kohn theorem does not so much form the basis of DFT, but is rather the consequence of a more comprehensive mathematical framework. Such results are especially useful when it comes to the construction of generalized DFTs.
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