Geometric quantization and epistemically restricted theories: The continuous case

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 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].