On Light-like Deformations of the Poincar\'e Algebra

TL;DR

This paper explores the physical implications of light-like deformations of the Poincaré algebra caused by specific Drinfel'd twists, revealing nonlinear algebra structures and their effects on multi-particle states and observables.

Contribution

It introduces a detailed analysis of light-like deformations of the Poincaré algebra via Jordanian twists, highlighting the resulting nonlinear algebraic structures and their physical consequences.

Findings

Nonlinear algebras emerge from twist-deformed generators.

Bounded domains of generators are identified in some cases.

Multi-particle states exhibit associative nonlinear additivity.

Abstract

We investigate the observational consequences of the light-like deformations of the Poincar\'e algebra induced by the jordanian and the extended jordanian classes of Drinfel'd twists. Twist-deformed generators belonging to a Universal Enveloping Algebra close nonlinear algebras. In some cases the nonlinear algebra is responsible for the existence of bounded domains of the deformed generators. The Hopf algebra coproduct implies associative nonlinear additivity of the multi-particle states. A subalgebra of twist-deformed observables is recovered whenever the twist-deformed generators are either hermitian or pseudo-hermitian with respect to a common invertible hermitian operator.