Operator Representations on Quantum Spaces

TL;DR

This paper provides explicit formulas for q-differentiation on quantum spaces like q-deformed Minkowski and Euclidean spaces, generalizing Jackson's q-derivative to higher dimensions, with potential applications in physics.

Contribution

It introduces explicit formulae for q-differentiation on quantum spaces, extending Jackson's q-derivative to three and four dimensions.

Findings

Explicit q-differentiation formulas for quantum spaces

Generalization of Jackson's q-derivative to higher dimensions

Potential applications in physics and quantum geometry

Abstract

In this article we present explicit formulae for q-differentiation on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. The calculations are based on the covariant differential calculus of these quantum spaces. Furthermore, our formulae can be regarded as a generalization of Jackson's q-derivative to three and four dimensions.