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 $ G\rightrightarrows \Omega $ 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 $ G $, 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.

中文翻译：

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Schwinger 的量子力学图景：2-groupoids 和对称性

从 Schwinger 的量子力学图片的群形方法开始，提出了在该框架中描述对称性的建议。结果表明，给定与（量子）系统相关的 groupoid $ G\rightrightarrows \Omega $，对其对称性有两种可能的描述，一种是“微观的”，另一种是“全局的”。微观的观点导致在 grupoid $ G $ 上引入了一个附加层，从而产生了一个合适的 2-groupoid 代数结构。另一方面，利用给定 groupoid 的二分群的概念，全局视角允许从 2-groupoid 构造一组对称。后一个概念允许引入 Wigner' 的模拟