5D Differential Calculus and Noether Analysis of Translation Symmetries in kappa-Minkowski Noncommutative Spacetime

TL;DR

This paper develops a Noether analysis for translation symmetries in 4D kappa-Minkowski noncommutative spacetime using a 5D differential calculus, deriving explicit conserved charges and proposing an intuitive basis for time derivatives.

Contribution

It introduces a novel 5D differential calculus framework for analyzing translation symmetries in kappa-Minkowski spacetime, providing explicit conserved charges and a new basis for understanding time derivatives.

Findings

Derived explicit formulas for conserved charges.

Proposed a basis leading to an intuitive time derivative description.

Enhanced understanding of translation symmetries in noncommutative spacetime.

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. Taking properly into account the properties of the differential calculus we arrive at an explicit formula for the conserved charges. We also propose a choice of basis for the 5D calculus which leads to an intuitive description of time derivatives.