Causality in Schwinger's Picture of Quantum Mechanics

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.This researchwas funded by the Spanish Ministry of Economy and Competitiveness (MINECO), through the Severo Ochoa Programme for Centres of Excellence in RD (SEV-2015/0554), the MINECO research project PID2020-117477GB-I00, the Comunidad de Madrid project QUITEMAD+, S2013/ICE- 2801, the CONEX-Plus programme (University Carlos III of Madrid), Marie Sklodowska-Curie COFUND Action (H2020-MSCA-COFUND-2017-GA 801538). This work has been supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of “Research Funds for Beatriz Galindo Fellowships” (C&QIG-BG-CM-UC3M), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation)