Causality in Schwinger's Picture of Quantum Mechanics Articles uri icon

publication date

  • January 2022

start page

  • 75

end page

  • 92

issue

  • 1

volume

  • 24

International Standard Serial Number (ISSN)

  • 1099-4300

abstract

  • 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.

keywords

  • causal categories; causal sets; causality; groupoids; incidence algebras; triangular algebras; von neumann algebras