Generalization of electrical resistance scaling to Dirac fields on perforated fractals
General Physics
2023-11-07 v1
Abstract
I construct perforated, "take-away" fractals that support short-distance power-law scaling with complex exponents for Dirac (spin-1/2) propagators. The construction relies on a fortuitous ansatz for Dirac boundary conditions at the surfaces of spherical voids in a three-dimensional embedding space, and requires that boundary conditions vary from void to void and are distributed statistically. The appropriate distribution can ensure that nonzero charges (but not dipoles, which drive nontrivial power-law scaling) induced in voids cancel out in spatial averaging.
Keywords
Cite
@article{arxiv.2311.02111,
title = {Generalization of electrical resistance scaling to Dirac fields on perforated fractals},
author = {Jonathan F. Schonfeld},
journal= {arXiv preprint arXiv:2311.02111},
year = {2023}
}
Comments
To be published in Fractals (World Scientific)