Duality Principle and Braided Geometry

TL;DR

This paper explores a new symmetry in physics between observables and states, utilizing Hopf algebras and quantum geometry, with implications for Planck scale physics and braided structures.

Contribution

It introduces a novel duality principle in braided geometry and extends it to semiclassical Poisson-Lie groups, advancing the understanding of quantum symmetries.

Findings

Identifies a new symmetry between observables and states.

Extends duality concepts to semiclassical Poisson-Lie groups.

Develops the framework of braided geometry in quantum physics.

Abstract

We give an overview of a new kind symmetry in physics which exists between observables and states and which is made possible by the language of Hopf algebras and quantum geometry. It has been proposed by the author as a feature of Planck scale physics. More recent work includes corresponding results at the semiclassical level of Poisson-Lie groups and at the level of braided groups and braided geometry.