Differential algebras on kappa-Minkowski space and action of the Lorentz algebra

TL;DR

This paper introduces two new differential algebra families on kappa-Minkowski space, utilizing novel realizations of the Lorentz algebra with Grassmann variables, achieving covariant actions without extra cotangent directions.

Contribution

It presents new differential algebra constructions and a novel Lorentz algebra realization that enables covariant actions directly on kappa-Minkowski space.

Findings

Two families of differential algebras constructed using formal power series.

A new realization of the Lorentz algebra with Grassmann variables.

Covariant action of Lorentz algebra on kappa-Minkowski space without extra directions.

Abstract

We propose two families of differential algebras of classical dimension on kappa-Minkowski space. The algebras are constructed using realizations of the generators as formal power series in a Weyl super-algebra. We also propose a novel realization of the Lorentz algebra so(1,n-1) in terms of Grassmann-type variables. Using this realization we construct an action of so(1,n-1) on the two families of algebras. Restriction of the action to kappa-Minkowski space is covariant. In contrast to the standard approach the action is not Lorentz covariant except on constant one-forms, but it does not require an extra cotangent direction.