Towards an axiomatic noncommutative geometry of quantum space and time

TL;DR

This paper proposes an axiomatic framework for quantum space and time, modeling space as a topological manifold and time as reconfiguration events, using noncommutative geometry concepts.

Contribution

It introduces a novel axiomatic approach to noncommutative geometry applied to quantum space-time, linking geometric structures with physical reconfiguration events.

Findings

Axiomatic model of quantum space as a topological manifold

Representation of time as reconfiguration events

Connection between noncommutative tangent bundles and physical space-time

Abstract

By exploring a possible physical realisation of the geometric concept of noncommutative tangent bundle, we outline an axiomatic quantum picture of space as topological manifold and time as a count of its reconfiguration events.