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arXiv · 2602.17273

On $\mathscr{T}$-based orthomodular dynamic algebras

Jan Paseka·Juanda Kelana Putra·Richard Smolka
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Abstract

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.

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Jan Paseka, Juanda Kelana Putra, Richard Smolka. 2026-02-19. On $\mathscr{T}$-based orthomodular dynamic algebras. https://arxiv.org/abs/2602.17273

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