Publication: Causality in Schwinger's Picture of Quantum Mechanics
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2022-01-01
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MDPI AG
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Abstract
This paper begins the study of the relation between causality and quantum mechanics, taking
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.
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Causal categories, Causal sets, Causality, Groupoids, Incidence algebras, Triangular algebras, Von neumann algebras
Bibliographic citation
Ciaglia, F. M., Di Cosmo, F., Ibort, A., Marmo, G., Schiavone, L., & Zampini, A. (2022). Causality in Schwinger’s Picture of Quantum Mechanics. In Entropy, 24(1), 75-92