From noncommutative space-time to quantum relativistic symmetries with fundamental mass parameter

TL;DR

This paper explores $$-deformations of space-time algebra, focusing on quantum relativistic symmetries with a fundamental mass parameter, and discusses their mathematical formalism and potential astrophysical applications.

Contribution

It provides a detailed analysis of $$-deformations of Minkowski space and extends the formalism to conformal and light-like cases, highlighting their physical implications.

Findings

$$-deformations can be applied along any Minkowski space direction

Formalism of $$-deformations is developed and clarified

Potential astrophysical applications of $$-deformed symmetries are discussed

Abstract

We consider the simplest class of Lie-algebraic deformations of space-time algebra, with the selection of $\kappa$-deformations as providing quantum deformation of relativistic framework. We recall that the $\kappa$-deformation along any direction in Minkowski space can be obtained. Some problems of the formalism of $\kappa$-deformations will be considered. We shall comment on the conformal extension of light-like $\kappa$-deformation as well as on the applications to astrophysical problems.