A symmetry invariant integral on kappa-deformed spacetime

TL;DR

This paper introduces a symmetry-invariant integral on kappa-deformed spacetime using algebraic methods, addressing a key challenge in defining integrals compatible with deformed symmetries.

Contribution

It proposes a new integral definition based on differential forms and demonstrates its invariance under the deformed symmetry structure.

Findings

Integral is explicitly invariant under deformed symmetries

Uses both constructive and Hopf algebraic methods

Addresses the gap in defining integrals on kappa-deformed spacetime

Abstract

In this note we present an approach using both constructive and Hopf algebraic methods to contribute to the not yet fully satisfactory definition of an integral on kappa-deformed spacetime. The integral presented here is based on the inner product of differential forms and it is shown that this integral is explicitly invariant under the deformed symmetry structure.