Quantum Geometry and the Planck Scale

TL;DR

This paper explores quantum geometry derived from quantum groups, highlighting implications for Planck scale physics, including generalized duality, fractional statistics, and the role of the conformal group.

Contribution

It introduces new aspects of noncommutative quantum geometry related to quantum groups and their relevance to Planck scale phenomena.

Findings

Generalized Fourier and wave-particle duality on curved spaces

Emergence of particles with fractional or braid statistics

Significant role of the conformal group in quantum geometry

Abstract

We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces emerges. Another feature is the need for particles with fractional or braid statistics. The conformal group also has a special role.