Remarks on Quantum Physics and Noncommutative Geometry

TL;DR

This paper proposes a novel mathematical framework using noncommutative geometry and category theory to model quantum mechanics, reconstructing space-time from quiver spectra and analyzing interference experiments.

Contribution

It introduces a new approach linking noncommutative geometry and category theory to quantum physics, focusing on spectra of path categories and their physical implications.

Findings

Model of quantum events via noncommutative ideals

Reconstruction of space-time from quiver spectra

Analysis of interference experiments within the framework

Abstract

The "quantum-event / prime ideal in a category/ noncommutative-point" alternative to "classical-event / commutative prime ideal/ point" is suggested. Ideals in additive categories, prime spectra and representation of quivers are considered as mathematical tools appropriate to model quantum mechanics. The space-time framework is to be reconstructed from the spectrum of the path category of a quiver. The interference experiment is considered as an example.