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Schwinger's Picture of Quantum Mechanics I: Groupoids

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arxiv 1905.12274 v1 pith:DVTHUNQ5 submitted 2019-05-29 math-ph hep-thmath.MPquant-ph

Florio M. Ciaglia , Alberto Ibort , Giuseppe Marmo This is my paper
classification math-phhep-thmath.MPquant-ph
keywords groupoidspicturebackgroundmechanicspresentedquantumschwingertheory
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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.

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  1. Fractional Quantum Hall Anyons via the Algebraic Topology of Exotic Flux Quanta

    cond-mat.mes-hall 2025-05 conditional novelty 6.0 of 10

    Fractional quantum Hall anyons are re-derived from a non-Lagrangian flux quantization in 2-Cohomotopy, with new predictions for torus degeneracy and defect anyons.

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