On Twist Quantizations of D=4 Lorentz and Poincare Algebras

TL;DR

This paper explores a nonstandard quantum deformation of the D=4 Lorentz and Poincare algebras using twist quantization, providing explicit formulas for deformed coproducts and antipodes in terms of physical generators.

Contribution

It introduces a novel twist deformation of D=4 Lorentz and Poincare algebras based on Jordanian deformation, extending previous algebraic structures with explicit physical representations.

Findings

Derived deformed coproducts and antipodes in terms of Lorentz generators

Extended the deformation to the Poincare algebra with a dimensionless parameter

Provided explicit mathematical framework for nonstandard quantum deformations

Abstract

We use the decomposition of o(3,1)=sl(2;C)_1\oplus sl(2;C)_2 in order to describe nonstandard quantum deformation of o(3,1) linked with Jordanian deformation of sl(2;C}. Using twist quantization technique we obtain the deformed coproducts and antipodes which can be expressed in terms of real physical Lorentz generators. We describe the extension of the considered deformation of D=4 Lorentz algebra to the twist deformation of D=4 Poincare algebra with dimensionless deformation parameter.