On non-commutativity in quantum theory (III): determinantal point processes and non-relativistic quantum mechanics

TL;DR

This paper explores the role of non-commutativity in quantum theory by analyzing point processes, leading to a new model that recovers non-relativistic quantum mechanics in a specific limit.

Contribution

It introduces a generalized point process-based model that extends previous work and connects non-commutative models to standard quantum mechanics.

Findings

Re-analysed model B using point process theory

Developed a new model C with modified space process

Recovered non-relativistic quantum mechanics in a limit

Abstract

This article concludes our critical analysis on the role of non-commutativity in quantum theory. After a brief introduction of the necessary notions on point processes, we re-analyse model B proposed in "On non-commutativity in quantum theory (II): toy models for non-commutative kinematics", using the point process theory. This viewpoint allows to generalize and modify the space process of model B in a simple manner, obtaining a new model (model C). This new model allows the recovery of non-relativistic quantum mechanics in a suitable limit.