Dirac-Fermions with interaction are considered directly by means of a simple Density Functional being the main concern the background energy as a function of the spatial dimension (fractional or not). The background energy grows as the dimension continuously rises. Comparison between the interacting and the non-interacting parts suggests that, around dimension two, both contributions are important. On the contrary, for dimensions other than two, interacting effects seem partially eclipsed (screening). Further, thermodynamics aspects related to dimension uncertainties are considered. Additionally, a massive branch appears.

中文翻译：

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Dirac-Fermions函数用于任意（分数）维的库仑相互作用：能量和压力

通过简单的密度泛函直接考虑具有相互作用的狄拉克-费米子，而密度泛函是主要关注的背景能量随空间维数（分数或非分数）的函数。随着尺寸的不断增加，背景能量也随之增加。相互作用部分和非相互作用部分之间的比较表明，在第二维附近，这两种贡献都很重要。相反，对于除两个以外的尺寸，相互作用的效果似乎被部分掩盖了（屏蔽）。此外，考虑了与尺寸不确定性有关的热力学方面。此外，还会出现一个巨大的分支。