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arXiv · 1803.05113

Star product on $L^2(S^n)$, $n = 2, 3, 5$

Erik Ignacio Díaz-Ortíz
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Abstract

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.

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Erik Ignacio Díaz-Ortíz. 2018-03-14. Star product on $L^2(S^n)$, $n = 2, 3, 5$. https://arxiv.org/abs/1803.05113

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