Dynamical maps and symmetroids

• URL: http://arxiv.org/abs/2205.06734v1
• Date: Fri, 13 May 2022 16:10:30 GMT
• Title: Dynamical maps and symmetroids
• Authors: Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort and Giuseppe Marmo
• Abstract summary: The issue of describing dynamical maps in the groupoidal approach to Quantum Mechanics is addressed. After inducing a Haar measure on the canonical symmetroid $mathcalS(G)$, the associated von-Neumann groupoid algebra is constructed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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