On $\mathscr{T}$-based orthomodular dynamic algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913003564171264 |
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| author | Paseka, Jan Putra, Juanda Kelana Smolka, Richard |
| author_facet | Paseka, Jan Putra, Juanda Kelana Smolka, Richard |
| contents | This paper establishes a categorical equivalence between the category $\mathbb{COL}$ of complete orthomodular lattices and the category $\mathscr{T}\mathbb{ODA}$ of $\mathscr{T}$-based orthomodular dynamic algebras. Complete orthomodular lattices serve as the static algebraic foundation for quantum logic, modeling the testable properties of quantum systems. In contrast, $\mathcal{T}$-based orthomodular dynamic algebras, which are specialized unital involutive quantales, formalize the composition and quantum-logical properties of quantum actions.
This result refines prior connections between orthomodular lattices and dynamic algebras, provides a constructive bridge between static and dynamic quantum logic perspectives, and extends naturally to Hilbert lattices and broader quantum-theoretic structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17273 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On $\mathscr{T}$-based orthomodular dynamic algebras Paseka, Jan Putra, Juanda Kelana Smolka, Richard Logic Rings and Algebras 81P10, 03G12, 06F07, 06B15 F.4.1; F.1.3 This paper establishes a categorical equivalence between the category $\mathbb{COL}$ of complete orthomodular lattices and the category $\mathscr{T}\mathbb{ODA}$ of $\mathscr{T}$-based orthomodular dynamic algebras. Complete orthomodular lattices serve as the static algebraic foundation for quantum logic, modeling the testable properties of quantum systems. In contrast, $\mathcal{T}$-based orthomodular dynamic algebras, which are specialized unital involutive quantales, formalize the composition and quantum-logical properties of quantum actions. This result refines prior connections between orthomodular lattices and dynamic algebras, provides a constructive bridge between static and dynamic quantum logic perspectives, and extends naturally to Hilbert lattices and broader quantum-theoretic structures. |
| title | On $\mathscr{T}$-based orthomodular dynamic algebras |
| topic | Logic Rings and Algebras 81P10, 03G12, 06F07, 06B15 F.4.1; F.1.3 |
| url | https://arxiv.org/abs/2602.17273 |