| Title:
|
On a higher spin generalization of the complex $\Pi $-operator (English) |
| Author:
|
Cheng, Wanqing |
| Author:
|
Ding, Chao |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
62 |
| Issue:
|
3 |
| Year:
|
2026 |
| Pages:
|
89-111 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. Bureš et al. generalized it to arbitrary spin $k/2$ in 2002 in the context of Clifford algebras. In this article, we introduce a higher spin $\Pi $-operator related to the Rarita-Schwinger operator. Further, we investigate norm estimates, mapping properties and the adjoint operator of the higher spin $\Pi $-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 $\Pi $-operator. (English) |
| Keyword:
|
Rarita-Schwinger operator |
| Keyword:
|
integral transform |
| Keyword:
|
higher spin $\Pi $-operator |
| Keyword:
|
higher spin Beltrami equation |
| MSC:
|
30G20 |
| MSC:
|
30G35 |
| MSC:
|
35A22 |
| DOI:
|
10.5817/AM2026-3-89 |
| . |
| Date available:
|
2026-08-25T08:26:21Z |
| Last updated:
|
2026-08-25 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153721 |
| . |
