A Dirac-Fermions functional for Coulomb interaction on arbitrary (fractional) dimension: Energy and pressure

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.