From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality

TL;DR

This paper re-examines Yang's quantized space-time model and its relation to Snyder's model and de Sitter special relativity, revealing their duality through a comprehensive classical and quantum analysis.

Contribution

It introduces a complete Yang model derived from a 5+1-dimensional Mink space, establishing the existence of Snyder's model, de Sitter relativity, and their duality.

Findings

Existence of Snyder's model within the Yang framework

Demonstration of UV-IR duality between models

Classical and quantum formulations of the complete Yang model

Abstract

By means of Dirac procedure, we re-examine Yang's quantized space-time model, its relation to Snyder's model, the de Sitter special relativity and their UV-IR duality. Starting from a dimensionless dS_5-space in a 5+1-d Mink-space a complete Yang model at both classical and quantum level can be presented and there really exist Snyder's model, the dS special relativity and the duality.