GENERALIZATION OF ELECTRICAL RESISTANCE SCALING TO DIRAC FIELDS ON PERFORATED FRACTALS

Jonathan F. Schonfeld ()
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Jonathan F. Schonfeld: Center for Astrophysics, Harvard and Smithsonian, 60 Garden St., Cambridge, Massachusetts 02138, United States

FRACTALS (fractals), 2023, vol. 31, issue 09, 1-7

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: Fractals; Sierpinski Carpet; Menger Sponge; Power-Law Scaling; Fractal Dimension; Dielectric Theory; Dirac Equation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23501086

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