Quantum Logic and Geometric Quantization

Abstract

We assume that M is a phase space and  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 "asymptotics quantum probability space" for the Hilbert lattice ( )  .

Prequantization, Geometric Quantization, Corrected Geometric Quantization

“…This possibility sure is not the end of the history, as other approaches show this is not the only "via regia" (the literature regarding other quantization methods is omitted here due to the large amount to be taken into consideration). A last work that we cite is [13] where the author studied the connection between the geometric quantization (GQ) process and the quantum logic (QL). In this optics, the geometric quantization can be a considered as a "machinery" that produces Hilbert spaces with interesting properties.…”

Geometric viewpoint on the quantization of a fuzzy logic

“…In more recent years the field of quantum logic has been related to a variety of abstract structures that generalize the archetypical lattice of projectors like orthomodular posets, orthoalgebras, effect algebras and categories [EGL07]. There are also several geometric approaches to quantum logic like [BW85] or the recent works [dCK16] and [Ca17].…”

Prequantization, geometric quantization, corrected geometric quantization

“…This possibility sure is not the end of the history as other approaches shows this is not the only "via regia" (the literature regarding other quantization methods is omitted here due to the large amount to be taken into consideration). A last work that we cite is [8] where the author studied the connection between the geometric quantization GQ process and the quantum logic QL. In this optics the geometric quantization can be a considered as a "machinery" that produces Hilbert spaces with interesting properties.…”