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    Effective trace framework for self-similar Casimir systems

    Goren Gordon*

    • *Contact author: goren@gorengordon.com

    Phys. Rev. D 113, 125013 – Published 15 June, 2026

    DOI: https://doi.org/10.1103/3x5c-4dyg

    Abstract

    The interaction of quantum fields with fractal and self-similar geometries encompasses multiple distinct physical regimes, including spectral geometry on intrinsic fractals, macroscopic self-similar Casimir configurations, and bounded Euclidean cavities with fractal boundaries. While the thermal equations of state and spectral asymptotics for these systems are well established, a cohesive treatment of the vacuum trace frequently conflates rigorous mathematical bounds with phenomenological models. In this manuscript, we systematically decouple these regimes and advance a unified effective framework combining the rigorous thermal trace of fractal radiation with a zero-temperature integrated vacuum trace for platelike self-similar geometries. We demonstrate that for systems governed by a scale-dependent Casimir coefficient C(ds,ln(d/ℓ*)), the anisotropic stress-energy tensor produces an integrated vacuum trace proportional to its logarithmic running, ∂ln dC. We strictly differentiate this effective macroscopic backreaction from first-principles local trace anomalies on genuine fractal boundaries. Finally, we analyze finite-level (n) prefractal realizations, establishing the analytical prerequisites necessary to transition this effective formalism into a quantitatively predictive electromagnetic theory amenable to experimental verification.

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