Classical basis for kappa-Poincare algebra and doubly special relativity theories

TL;DR

This paper explores different formulations of the kappa-Poincare algebra, providing classical basis representations and modifications that relate to Doubly Special Relativity, enhancing understanding of quantum spacetime symmetries.

Contribution

It introduces two formulations of kappa-Poincare algebra, including a classical basis and a modified version with an extra generator, linking to DSR and relativistic quantum mechanics.

Findings

Complete Hopf algebra formulas in classical Poincare basis

Elimination of non-polynomial functions in kappa-parameter

Hilbert space representations connect DSR to relativistic quantum mechanics

Abstract

Several issues concerning quantum kappa-Poincare algebra are discussed and reconsidered here. We propose two different formulations of kappa-Poincare quantum algebra. Firstly we present a complete Hopf algebra formulae of kappa-Poincare in classical Poincare basis. Further by adding one extra generator, which modifies the classical structure of Poincare algebra, we eliminate non polynomial functions in the kappa-parameter. Hilbert space representations of such algebras make Doubly Special Relativity (DSR) similar to the Stueckelberg's version of (proper-time) relativistic Quantum Mechanics.