Geometric Quantization and Epistemically Restricted Theories: The Continuous Case

TL;DR

This paper explores how to derive quantum-like features from classical theories with epistemic restrictions using symplectic geometry, leading to a C*-algebraic formulation and Moyal quantization for continuous variables.

Contribution

It introduces a symplectic geometric framework to formulate epistemically restricted theories as twisted group C*-algebras, connecting classical and quantum formalisms.

Findings

Derivation of a C*-algebraic formulation for epistemic restrictions.

Application of groupoid quantization to continuous variables.

Recovery of Moyal quantization from classical symplectic structures.

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].