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Schwinger's picture of Quantum Mechanics

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arxiv 2002.09326 v1 pith:MQKVDZWE submitted 2020-02-21 math-ph math.MPquant-ph

classification math-phmath.MPquant-ph
keywords approachbasiccalledgroupoidmechanicsquantumschwingeralgebraic
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In this paper we will present tha main features of what can be called Schwinger's foundational approach to Quantum Mechanics. The basic ingredients of this formulation are the \textit{selective measurements}, whose algebraic composition rules define a mathematical structure called groupoid, which is associated with any physical system. After the introduction of the basic axioms of a groupoid, the concepts of observables and states, statistical interpretation and evolution are derived. An example is finally introduced to support the theoretical description of this approach.

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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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