The q-Dirac Operator on Quantum Euclidean Space

2025/04/13 by Bernstein, Swanhild, Zimmermann, Martha Lina, Schneider, Baruch
#30G35 #39A70 #81R99 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.09569

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(\frako)-invariant Laplacian Δ_q. Due to the non-commutativity of the multiplication, we need a special Clifford algebra Cℓ_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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