Some consequences of a noncommutative space-time structure

TL;DR

This paper explores the implications of a fundamental length scale arising from noncommutative space-time, predicting measurable effects like phase-space modifications and spectrum corrections in physical phenomena.

Contribution

It introduces a mathematically well-defined noncommutative space-time model with specific experimental predictions, advancing understanding of fundamental length implications.

Findings

Phase-space volume modifications affecting particle interactions

Corrections to Coulomb spectrum calculations

Relevance for GZK sphere energy cutoff

Abstract

The existence of a fundamental length (or fundamental time) has been conjecture in many contexts. Here one discusses some consequences of a fundamental constant of this type, which emerges as a consequence of deformation-stability considerations leading to a non-commutative space-time structure. This mathematically well defined structure is sufficiently constrained to allow for unambiguous experimental predictions. In particular one discusses the phase-space volume modifications and their relevance for the calculation of the GZK sphere. Corrections to the spectrum of the Coulomb problemb are also computed.