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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1803.05113 |
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| _version_ | 1866916644661493760 |
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| author | Díaz-Ortíz, Erik Ignacio |
| author_facet | Díaz-Ortíz, Erik Ignacio |
| contents | We consider the bounded linear operators with domain in the Hilbert space $L^2(S^n)$, $n=2,3,5$ and describe its symbolic calculus defined by the Berezin quantization. In particular, we derive an explicit formula for the composition of Berezin's symbols and thus a noncommutative invariant star product, which in turn is invariant under the action of the group $SU(2)$, $SU(2)\times SU(2)$ and $SU(4)$ on $\mathbb C^2$ , $\mathbb C^4$ and $\mathbb C^8$ respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1803_05113 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Star product on $L^2(S^n)$, $n = 2, 3, 5$ Díaz-Ortíz, Erik Ignacio Mathematical Physics We consider the bounded linear operators with domain in the Hilbert space $L^2(S^n)$, $n=2,3,5$ and describe its symbolic calculus defined by the Berezin quantization. In particular, we derive an explicit formula for the composition of Berezin's symbols and thus a noncommutative invariant star product, which in turn is invariant under the action of the group $SU(2)$, $SU(2)\times SU(2)$ and $SU(4)$ on $\mathbb C^2$ , $\mathbb C^4$ and $\mathbb C^8$ respectively. |
| title | Star product on $L^2(S^n)$, $n = 2, 3, 5$ |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/1803.05113 |