q-Exponentials on quantum spaces

TL;DR

This paper derives explicit formulas for q-exponentials on various quantum spaces, including q-deformed Minkowski and Euclidean spaces, extending the classical q-exponential to higher-dimensional quantum geometries.

Contribution

It provides new explicit formulae for q-exponentials on quantum spaces, which are useful in physics and generalize known q-exponentials to higher dimensions.

Findings

Explicit formulae for q-exponentials on quantum Minkowski space

Explicit formulae for q-exponentials on quantum Euclidean spaces in 2, 3, and 4 dimensions

Potential applications in physics involving quantum space symmetries

Abstract

We present explicit formulae for q-exponentials on quantum spaces which could be of particular importance in physics, i.e. the q-deformed Minkowski-space and the q-deformed Euclidean space with two, three or four dimensions. Furthermore, these formulae can be viewed as 2-, 3- or 4-dimensional analogues of the well-known q-exponential function.