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Keywords = symplectic groupoid

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17 pages, 332 KB  
Review
Quantum Orbit Method in the Presence of Symmetries
by Nicola Ciccoli
Symmetry 2021, 13(4), 724; https://doi.org/10.3390/sym13040724 - 19 Apr 2021
Cited by 1 | Viewed by 2549
Abstract
We review some of the main achievements of the orbit method, when applied to Poisson–Lie groups and Poisson homogeneous spaces or spaces with an invariant Poisson structure. We consider C-algebra quantization obtained through groupoid techniques, and we try to put the [...] Read more.
We review some of the main achievements of the orbit method, when applied to Poisson–Lie groups and Poisson homogeneous spaces or spaces with an invariant Poisson structure. We consider C-algebra quantization obtained through groupoid techniques, and we try to put the results obtained in algebraic or representation theoretical contexts in relation with groupoid quantization. Full article
(This article belongs to the Special Issue Quantum Group Symmetry and Quantum Geometry)
20 pages, 379 KB  
Article
A Functorial Construction of Quantum Subtheories
by Ivan Contreras and Ali Nabi Duman
Entropy 2017, 19(5), 220; https://doi.org/10.3390/e19050220 - 11 May 2017
Viewed by 5012
Abstract
We apply the geometric quantization procedure via symplectic groupoids to the setting of epistemically-restricted toy theories formalized by Spekkens (Spekkens, 2016). In the continuous degrees of freedom, this produces the algebraic structure of quadrature quantum subtheories. In the odd-prime finite degrees of freedom, [...] Read more.
We apply the geometric quantization procedure via symplectic groupoids to the setting of epistemically-restricted toy theories formalized by Spekkens (Spekkens, 2016). In the continuous degrees of freedom, this produces the algebraic structure of quadrature quantum subtheories. In the odd-prime finite degrees of freedom, we obtain a functor from the Frobenius algebra of the toy theories to the Frobenius algebra of stabilizer quantum mechanics. Full article
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
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