Schwinger's Picture of Quantum Mechanics I: Groupoids

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 d...

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Bibliographic Details
Published in:arXiv.org 2019-05
Main Authors: Ciaglia, Florio M, Ibort, Alberto, Marmo, Giuseppe
Format: Article
Language:English
Subjects:
Pictures
Quantum mechanics
Quantum physics
Quantum theory
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1905.12274