Differential structure on the $\kappa$-Minkowski spacetime from twist

TL;DR

This paper develops a four-dimensional differential calculus for the twist-deformed $ kappa$-Minkowski spacetime, avoiding the need for an extra dimension, and extends the approach to arbitrary dimensions.

Contribution

It introduces a four-dimensional differential structure for twist-deformed $ kappa$-Minkowski spacetime that is closed in four dimensions, unlike previous bicovariant calculus approaches.

Findings

Differential structure is closed in four dimensions.

Construction applicable to arbitrary dimensional spacetimes.

Avoids need for extra fifth dimension in calculus.

Abstract

We study four dimensional $\kappa$-Minkowski spacetime constructed by the twist deformation of $U(igl(4,R))$. We demonstrate that the differential structure of such twist-deformed $\kappa$-Minkowski spacetime is closed in four dimensions contrary to the construction of $\kappa$-Poincar\'{e} bicovariant calculus which needs an extra fifth dimension. Our construction holds in arbitrary dimensional spacetimes.