kappa-Minkowski representations on Hilbert spaces

TL;DR

This paper studies the algebra of functions on kappa-Minkowski noncommutative spacetime by constructing and classifying its Hilbert space representations, leading to a natural operator trace-based integration method.

Contribution

It introduces a novel approach to represent and classify the algebra of kappa-Minkowski spacetime on Hilbert spaces, enabling a new integration framework.

Findings

Constructed and classified representations of the algebra

Developed a trace-based integration method

Provided a new operator-theoretic perspective

Abstract

The algebra of functions on kappa-Minkowski noncommutative spacetime is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction of integration in kappa-Minkowski spacetime in terms of the usual trace of operators.