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arXiv · 2504.09569

The $q$-Dirac Operator on Quantum Euclidean Space

Swanhild Bernstein·Martha Lina Zimmermann·Baruch Schneider
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Abstract

This paper provides the foundations of quantum Clifford analysis in $q$-commutative variables with symmetric difference operators. We consider a $q$-Dirac operator on the quantum Euclidean space that factorizes the $U_q(\frak{o})$-invariant Laplacian $\Delta_q.$ Due to the non-commutativity of the multiplication, we need a special Clifford algebra $C\ell_{0,n}^q.$ We define $q$-monogenic functions as null solutions of the $q$-Dirac operator and $q$-spherical monogenic functions. We define an inner Fischer product and decompose the space of homogeneous polynomials of degree $k.$

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Swanhild Bernstein, Martha Lina Zimmermann, Baruch Schneider. 2025-04-13. The $q$-Dirac Operator on Quantum Euclidean Space. https://arxiv.org/abs/2504.09569

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