The $q$-Dirac Operator on Quantum Euclidean Space
Complex Variables
2025-04-15 v1
Abstract
This paper provides the foundations of quantum Clifford analysis in -commutative variables with symmetric difference operators. We consider a -Dirac operator on the quantum Euclidean space that factorizes the -invariant Laplacian Due to the non-commutativity of the multiplication, we need a special Clifford algebra We define -monogenic functions as null solutions of the -Dirac operator and -spherical monogenic functions. We define an inner Fischer product and decompose the space of homogeneous polynomials of degree
Cite
@article{arxiv.2504.09569,
title = {The $q$-Dirac Operator on Quantum Euclidean Space},
author = {Swanhild Bernstein and Martha Lina Zimmermann and Baruch Schneider},
journal= {arXiv preprint arXiv:2504.09569},
year = {2025}
}
Comments
18 pages