The $q$-Dirac Operator on Quantum Euclidean Space
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913791468371968 |
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| author | Bernstein, Swanhild Zimmermann, Martha Lina Schneider, Baruch |
| author_facet | Bernstein, Swanhild Zimmermann, Martha Lina Schneider, Baruch |
| contents | 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 $Δ_q.$ 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 $k.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $q$-Dirac Operator on Quantum Euclidean Space Bernstein, Swanhild Zimmermann, Martha Lina Schneider, Baruch Complex Variables 30G35, 81R99, 39A70 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 $Δ_q.$ 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 $k.$ |
| title | The $q$-Dirac Operator on Quantum Euclidean Space |
| topic | Complex Variables 30G35, 81R99, 39A70 |
| url | https://arxiv.org/abs/2504.09569 |