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arXiv · 2205.06734

Dynamical maps and symmetroids

Florio M. Ciaglia·Fabio Di Cosmo·Alberto Ibort·Giuseppe Marmo
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Abstract

Starting from the canonical symmetroid $\mathcal{S}(G)$ associated with a groupoid $G$, the issue of describing dynamical maps in the groupoidal approach to Quantum Mechanics is addressed. After inducing a Haar measure on the canonical symmetroid $\mathcal{S}(G)$, the associated von-Neumann groupoid algebra is constructed. It is shown that the left-regular representation allows to define linear maps on the groupoid-algebra of the groupoid $G$ and given subsets of functions are associated with completely positive maps. Some simple examples are also presented.

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Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo. 2022-05-13. Dynamical maps and symmetroids. https://arxiv.org/abs/2205.06734

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