Effective Trace Framework for Self-Similar Casimir Systems
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910142830739456 |
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| author | Gordon, Goren |
| author_facet | Gordon, Goren |
| contents | 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 plate-like self-similar geometries. We demonstrate that for systems governed by a scale-dependent Casimir coefficient $C(d_s, \ln(d/\ell_*))$, the anisotropic stress-energy tensor produces an integrated vacuum trace proportional to its logarithmic running, $\partial_{\ln d}C$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_16693 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Effective Trace Framework for Self-Similar Casimir Systems Gordon, Goren Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory 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 plate-like self-similar geometries. We demonstrate that for systems governed by a scale-dependent Casimir coefficient $C(d_s, \ln(d/\ell_*))$, the anisotropic stress-energy tensor produces an integrated vacuum trace proportional to its logarithmic running, $\partial_{\ln d}C$. 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. |
| title | Effective Trace Framework for Self-Similar Casimir Systems |
| topic | Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.16693 |