论文标题
$ {\ mathbb {r}}^{4n} $和berezin-toeplitz运算符的扭曲器空间
The twistor space of ${\mathbb{R}}^{4n}$ and Berezin-Toeplitz operators
论文作者
论文摘要
Hyperkähler歧管$ m $具有由二维球$ s^2 \ cong \ mathbb {cp}^1 $索引的诱导复杂结构的家族。 $ m $的扭曲器空间是一个复杂的歧管$ tw（m）$，以及天然的全态投影$ tw（m）\ to \ mathbb {cp}^1 $，其在$ \ mathbb {cp}^1 $的每个点上的纤维是$ M $的副本，具有相应的诱导复杂结构。我们从该球体中删除一个点（对应于扭曲器空间中的一根光纤），对于$ m = \ mathbb {r}^{4n} $，$ n \ in \ mathbb {n} $，配备了与标准HyperKähler结构配置的，我们构建了一个量子，替代了berezin to poxizatiz to^poarniz to^poarniz to^to^poarniz to^aptritiz to^poxizatiz to^rityiz to^。 pt \} $。我们为此量化提供了半经典的渐近学。
A hyperkähler manifold $M$ has a family of induced complex structures indexed by a two-dimensional sphere $S^2 \cong \mathbb{CP}^1$. The twistor space of $M$ is a complex manifold $Tw(M)$ together with a natural holomorphic projection $Tw(M) \to \mathbb{CP}^1$, whose fiber over each point of $\mathbb{CP}^1$ is a copy of $M$ with the corresponding induced complex structure. We remove one point from this sphere (corresponding to one fiber in the twistor space),and for the case of $M = \mathbb{R}^{4n}$, $n\in\mathbb{N}$, equipped with the standard hyperkähler structure, we construct one quantization that replaces the family of Berezin-Toeplitz quantizations parametrized by $S^2-\{ pt\}$. We provide semiclassical asymptotics for this quantization.
