Generalized Q-Exponentials Related to Orthogonal Quantum Groups and Fourier Transformations of Noncommutative Spaces

TL;DR

This paper constructs a new q-exponential series linked to orthogonal quantum symmetries, enabling Fourier transformations between position and momentum spaces in q-deformed physics, and introduces q-plane wave solutions with noncommuting phases.

Contribution

It introduces a novel q-exponential function related to orthogonal quantum groups, facilitating Fourier analysis in noncommutative quantum spaces.

Findings

Developed a new q-special function for quantum symmetries

Derived q-plane wave solutions with noncommuting phases

Established Fourier transformation framework for q-deformed spaces

Abstract

An essential prerequisite for the study of q-deformed physics are particle states in position and momentum representation. In order to relate x- and p-space by Fourier transformations the appropriate q-exponential series related to orthogonal quantum symmetries is constructed. It turns out to be a new q-special function giving rise to q-plane wave solutions that transform with a noncommuting phase under translations.