Geometric Quantization and Epistemically Restricted Theories: The Continuous Case

Ivan Contreras
(University of Illinois at Urbana-Champain)
Ali Nabi Duman
(King Fahd University of Petroleum and Minerals)

It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have about an individual system [5, 18].These are so called epistemic restrictions. Such restrictions have been recently formulated in terms of the symplectic geometry of the corresponding classical theory [19]. The purpose of this note is to describe, using this symplectic framework, how to obtain a C*-algebraic formulation for the epistemically restricted theories. In the case of continuous variables, following the groupoid quantization recipe of E. Hawkins, we obtain a twisted group C*-algebra which is the usual Moyal quantization of a Poisson vector space [12].

In Ross Duncan and Chris Heunen: Proceedings 13th International Conference on Quantum Physics and Logic (QPL 2016), Glasgow, Scotland, 6-10 June 2016, Electronic Proceedings in Theoretical Computer Science 236, pp. 40–50.
10 pages.
Published: 1st January 2017.

ArXived at: http://dx.doi.org/10.4204/EPTCS.236.3 bibtex PDF

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