On the mathematical origin of quantum space-time

TL;DR

This paper explores the mathematical foundation of quantum space-time by linking Euclidean spaces to Schwartz distributions and proposing quantum deformations as a new perspective for integration in quantum models.

Contribution

It introduces a novel mathematical framework connecting Euclidean spaces with Schwartz distributions, suggesting quantum deformations for a deeper understanding of quantum space-time.

Findings

Euclidean space is homeomorphic to a subset of Schwartz distributions.

Smooth functions are extended onto the space of distributions.

Quantum deformations modify the integration process in quantum models.

Abstract

An Euclidean topological space E is homeomorphic to the subset of delta-functions of the space D'(E) of Schwartz distributions on E. Herewith, any smooth function of compact support on E is extended onto D'(E). One can think of these extensions as sue generis quantum deformations. In quantum models, one therefore should replace integration of functions over E with that over D(E).