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Generalization Of Electrical Resistance Scaling To Dirac Fields On Perforated Fractals

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  • JONATHAN F. SCHONFELD

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

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.

Suggested Citation

  • Jonathan F. Schonfeld, 2023. "Generalization Of Electrical Resistance Scaling To Dirac Fields On Perforated Fractals," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(09), pages 1-7.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:09:n:s0218348x23501086
    DOI: 10.1142/S0218348X23501086
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