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- W3163670560 abstract "<p style='text-indent:20px;'>Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced. It is shown that, given a groupoid <inline-formula><tex-math id=M1>begin{document}$ Grightrightarrows Omega $end{document}</tex-math></inline-formula> associated with a (quantum) system, there are two possible descriptions of its symmetries, one microscopic, the other one global. The microscopic point of view leads to the introduction of an additional layer over the grupoid <inline-formula><tex-math id=M2>begin{document}$ G $end{document}</tex-math></inline-formula>, giving rise to a suitable algebraic structure of 2-groupoid. On the other hand, taking advantage of the notion of group of bisections of a given groupoid, the global perspective allows to construct a group of symmetries out of a 2-groupoid. The latter notion allows to introduce an analog of the Wigner's theorem for quantum symmetries in the groupoid approach to Quantum Mechanics." @default.
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- W3163670560 date "2021-01-01" @default.
- W3163670560 modified "2023-10-16" @default.
- W3163670560 title "Schwinger's picture of quantum mechanics: 2-groupoids and symmetries" @default.
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- W3163670560 doi "https://doi.org/10.3934/jgm.2021008" @default.
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