The -Dirac Operator on Quantum Euclidean Space
arXiv:2504.09569
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
18 pages