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arXiv · 1603.02189

Geometric Quantization and Epistemically Restricted Theories: The Continuous Case

Ivan Contreras·Ali Nabi Duman
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Abstract

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].

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Ivan Contreras, Ali Nabi Duman. 2016-03-07. Geometric Quantization and Epistemically Restricted Theories: The Continuous Case. https://doi.org/10.4204/eptcs.236.3

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