A realization of the quantum Lorentz group

TL;DR

This paper constructs a quantum deformation of the Lorentz group, finding its irreducible representations that recover classical Lorentz group representations as the deformation parameter approaches 1.

Contribution

It provides a realization of the quantum Lorentz group and explicitly derives its irreducible representations, connecting them to classical Lorentz group representations.

Findings

Irreducible representations of the quantum Lorentz group are explicitly constructed.

In the limit as q approaches 1, these representations reduce to classical Lorentz group representations.

The paper advances understanding of quantum group symmetries in relativistic physics.

Abstract

A realization of a deformed Lorentz algebra is considered and its irreducible representations are found; in the limit $q\to 1$, these are precisely the irreducible representations of the classical Lorentz group.