Semiclassical algebraic reconstruction for type III algebras
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910216495300608 |
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| author | Zhong, Haocheng |
| author_facet | Zhong, Haocheng |
| contents | In this work, we address the unresolved type III cases of the algebraic reconstruction theorem by integrating crossed product algebras and semiclassical approximations. We first derive that the relative entropy in crossed product algebras factorizes into contributions from the original algebra and observer wavefunctions. By constructing ``holographic'' crossed product algebras for ``bulk'' and ``boundary'' type III factors, we extend the algebraic reconstruction theorem to include the algebraic Ryu-Takayanagi (RT) formula semiclassically, which provides a complete algebraic description of the reconstruction theorem, as an intrinsic framework for the algebraic version of bulk-boundary correspondences in holographic duality. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_13576 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semiclassical algebraic reconstruction for type III algebras Zhong, Haocheng High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics In this work, we address the unresolved type III cases of the algebraic reconstruction theorem by integrating crossed product algebras and semiclassical approximations. We first derive that the relative entropy in crossed product algebras factorizes into contributions from the original algebra and observer wavefunctions. By constructing ``holographic'' crossed product algebras for ``bulk'' and ``boundary'' type III factors, we extend the algebraic reconstruction theorem to include the algebraic Ryu-Takayanagi (RT) formula semiclassically, which provides a complete algebraic description of the reconstruction theorem, as an intrinsic framework for the algebraic version of bulk-boundary correspondences in holographic duality. |
| title | Semiclassical algebraic reconstruction for type III algebras |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2605.13576 |