English

Schwinger's Picture of Quantum Mechanics I: Groupoids

Mathematical Physics 2019-09-17 v1 High Energy Physics - Theory math.MP Quantum Physics

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-Schr\"odinger and Born-Jordan-Heisenberg pictures are succinctly discussed.

Keywords

Cite

@article{arxiv.1905.12274,
  title  = {Schwinger's Picture of Quantum Mechanics I: Groupoids},
  author = {Florio M. Ciaglia and Alberto Ibort and Giuseppe Marmo},
  journal= {arXiv preprint arXiv:1905.12274},
  year   = {2019}
}

Comments

32 pages. Comments are welcome!