Schwinger's picture of quantum mechanics I: Groupoids Articles uri icon

publication date

  • June 2019

issue

  • 8(1950119)

volume

  • 16

International Standard Serial Number (ISSN)

  • 0219-8878

Electronic International Standard Serial Number (EISSN)

  • 1793-6977

abstract

  • A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger's algebra of selective measurements and helps to understand its scope and eventual applications. In this first paper, the kinematical background is described using elementary notions from category theory, in particular the notion of 2-groupoids as well as their representations. Some basic results are presented, and the relation with the standard Dirac&-Schrödinger and Born&-Jordan&-Heisenberg pictures are succinctly discussed.

keywords

  • schwinger algebra; groupoids; groupoid algebra; c*-algebra; states; hamiltonian; dynamical flow