Kaydedildi:
| Asıl Yazarlar: | , |
|---|---|
| Materyal Türü: | Recurso digital |
| Dil: | İngilizce |
| Baskı/Yayın Bilgisi: |
Zenodo
2025
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| Online Erişim: | https://doi.org/10.5281/zenodo.18095301 |
| Etiketler: |
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İçindekiler:
- <p>Mathematical Applications of Science Fiction</p> <p>Abstract. We present a rigorous constructive framework for the perturbative control of the spectrum<br>of Dirac operators associated with non-unital spectral triples (A, H, D). By embedding the non-compact<br>manifold data into a sequence of finite-dimensional C*-algebraic lattices (Planck-scale approximations),<br>we derive explicit bounds on the eigenvalue shifts under inner fluctuations of the metric. We intro-<br>duce the Selene-Dirac Perturbation Series, a convergent expansion in the Banach space of bounded<br>operators, to engineer specific spectral gaps. Furthermore, we establish a descent mechanism in cyclic<br>cohomology, proving that the Chern-Connes character of the perturbed lattice system converges to the<br>topological invariants of the continuum limit in the weak-∗ topology. This provides a mechanism for<br>"finite-resolution" topological protection, with direct applications to error correction in quantum gravity<br>models and topological quantum computing.</p>