On the 5D differential calculus and translation transformations in 4D kappa-Minkowski noncommutative spacetime

TL;DR

This paper analyzes translation symmetries in 4D κ-Minkowski noncommutative spacetime using a 5D differential calculus, proposing a basis change for a clearer understanding of time translations.

Contribution

It demonstrates that existing 4D calculus techniques apply to 5D calculus and introduces a basis change that clarifies the structure of time translations in κ-Minkowski.

Findings

The 5D calculus basis often used overlooks aspects of time translation structure.

A new basis for the 5D calculus provides a more intuitive understanding of time translations.

Existing 4D calculus methods are applicable to 5D calculus without modification.

Abstract

We perform a Noether analysis for a description of translation transformations in 4D $\kappa$-Minkowski noncommutative spacetime which is based on the structure of a 5D differential calculus. The techniques that some of us had previously developed (hep-th/0607221) for a description of translation transformations based on a 4D differential calculus turn out to be applicable without any modification, and they allow us to show that the basis usually adopted for the 5D calculus does not take into account certain aspects of the structure of time translations in $\kappa$-Minkowski. We propose a change of basis for the 5D calculus which leads to a more intuitive description of time translations.