Schwinger's picture of quantum mechanics IV: Composition and independence Articles uri icon

publication date

  • March 2020


  • 4(2050058)


  • 17

International Standard Serial Number (ISSN)

  • 0219-8878

Electronic International Standard Serial Number (EISSN)

  • 1793-6977


  • The groupoid description of Schwinger's picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their independence. Physical subsystems have a neat algebraic description as subgroupoids of the Schwinger's groupoid of the system. The groupoid picture offers two natural notions of composition of systems: Direct and free products of groupoids, that will be analyzed in depth as well as their universal character. Finally, the notion of independence of subsystems will be reviewed, finding that the usual notion of independence, as well as the notion of free independence, find a natural realm in the groupoid formalism. The ideas described in this paper will be illustrated by using the EPRB experiment. It will be observed that, in addition to the notion of the non-separability provided by the entangled state of the system, there is an intrinsic "non-separability" associated to the impossibility of identifying the entangled particles as subsystems of the total system.


  • schwinger algebra; groupoids; groupoid algebra; c*-algebra; subgroupoids; direct product; free product; independence; free independence; eprb experiment