- Entropy (Entropy) Journal
- January 2022
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- This paper begins the study of the relation between causality and quantum mechanics, tak-ing advantage of the groupoidal description of quantum mechanical systems inspired by Schwinger's picture of quantum mechanics. After identifying causal structures on groupoids with a particular class of subcategories, called causal categories accordingly, it will be shown that causal structures can be recovered from a particular class of non-selfadjoint class of algebras, known as triangular operator algebras, contained in the von Neumann algebra of the groupoid of the quantum system. As a consequence of this, Sorkin's incidence theorem will be proved and some illustrative examples will be discussed.
- causal categories; causal sets; causality; groupoids; incidence algebras; triangular algebras; von neumann algebras