Quantum groups and deformed special relativity

TL;DR

This paper explores q-deformed Minkowski spaces, analyzing their algebraic structures, covariance properties, and potential physical implications within non-commutative geometry and quantum group frameworks.

Contribution

It develops detailed non-commutative differential calculi for q-Minkowski spaces and compares them with existing models, highlighting covariance and algebraic isomorphisms.

Findings

Demonstrates isomorphisms among space-time and derivative algebras

Develops covariance-preserving differential calculi for q-Minkowski spaces

Discusses physical implications and open problems in quantum spacetime models

Abstract

The structure and properties of possible $q$-Minkowski spaces is discussed, and the corresponding non-commutative differential calculi are developed in detail and compared with already existing proposals. This is done by stressing its covariance properties as described by appropriate reflection equations. Some isomorphisms among the space-time and derivative algebras are demonstrated, and their representations are described briefly. Finally, some physical consequences and open problems are discussed.