The higher spin $Π$-operator in Clifford analysis
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912949838282752 |
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| author | Cheng, Wanqing Ding, Chao |
| author_facet | Cheng, Wanqing Ding, Chao |
| contents | Rarita-Schwinger fields are solutions to the relativistic field equation of spin-$3/2$ fermions in four dimensional flat spacetime, which are important in supergravity and superstring theories. Bure\v s et al. generalized it to arbitrary spin $k/2$ in 2002 in the context of Clifford algebras. In this article, we introduce the higher spin $Π$-operator related to the Rarita-Schwinger operator. Further, we investigate norm estimates, mapping properties and the adjoint operator of the higher spin $Π$-operator. As an application, a higher spin Beltrami equation is introduced, and existence and uniqueness of solutions to this higher spin Beltrami equation is established by the norm estimate of the higher spin $Π$-operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11271 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The higher spin $Π$-operator in Clifford analysis Cheng, Wanqing Ding, Chao Complex Variables 30G35, 30G20, 35A22 Rarita-Schwinger fields are solutions to the relativistic field equation of spin-$3/2$ fermions in four dimensional flat spacetime, which are important in supergravity and superstring theories. Bure\v s et al. generalized it to arbitrary spin $k/2$ in 2002 in the context of Clifford algebras. In this article, we introduce the higher spin $Π$-operator related to the Rarita-Schwinger operator. Further, we investigate norm estimates, mapping properties and the adjoint operator of the higher spin $Π$-operator. As an application, a higher spin Beltrami equation is introduced, and existence and uniqueness of solutions to this higher spin Beltrami equation is established by the norm estimate of the higher spin $Π$-operator. |
| title | The higher spin $Π$-operator in Clifford analysis |
| topic | Complex Variables 30G35, 30G20, 35A22 |
| url | https://arxiv.org/abs/2508.11271 |