Quantum Logic and Geometric quantization

TL;DR

This paper explores the relationship between quantum logic and geometric quantization, proposing a new interpretation to construct an asymptotic quantum probability space linked to the Hilbert lattice.

Contribution

It introduces a novel interpretation connecting quantum logic with geometric quantization, leading to the construction of an asymptotic quantum probability space.

Findings

Established a model relating experimental propositions to geometric quantization

Developed an asymptotic quantum probability space for the Hilbert lattice

Provided new insights into the structure of quantum logic in phase space

Abstract

We assume that M is a phase space and H an Hilbert space yielded by a quantization scheme. In this paper we consider the set of all "experimental propositions" of M and we look for a model of quantum logic in relation to the quantization of the base manifold M. In particular we give a new interpretation about previous results of the author in order to build an "asymptotic quantum probability space" for the Hilbert lattice L(H).