论文标题
在均匀的紧凑型歧管上的Berezin型量化
Berezin-type quantization on even-dimensional compact manifolds
论文作者
论文摘要
在本文中，我们表明，可以通过删除较低尺寸的骨架$ m_0 $，以使剩下的剩余对$ r^{2d} $（细胞分解）来确定$ r^{2d} $ cpp^$ cpp^$ cpp^n in $ cpp^d $ cpp^n in $ cpp^d $ cpp^n in $ cp^d $ cpp^n in $ cp^d $ cpp^n n $ cp^d $ cpp^d $ cpp^从$ cp^d $诱导了当地的泊松结构和贝雷唱型量化。因此，我们有一个带有繁殖内核的希尔伯特空间。希尔伯特空间上有界线性算子的符号具有恒星产品，该恒星产品满足了一组零度零之外的对应力原理。这种结构取决于差异性。人们需要跟踪全球全体性，因此需要跟踪歧管的细胞分解。例如，我们说明了圆环的这种类型的Quanitzation。我们以与上述相同的精神表现出对复杂歧管的berezin-toeplitz量化。
In this article we show that a Berezin-type quantization can be achieved on a compact even dimensional manifold $M^{2d}$ by removing a skeleton $M_0$ of lower dimension such that what remains is diffeomorphic to $R^{2d}$ (cell decomposition) which we identify with $C^d$ and embed in $ CP^d$. A local Poisson structure and Berezin-type quantization are induced from $ CP^d$. Thus we have a Hilbert space with a reproducing kernel. The symbols of bounded linear operators on the Hilbert space have a star product which satisfies the correspondence principle outside a set of measure zero. This construction depends on the diffeomorphism. One needs to keep track of the global holonomy and hence the cell decomposition of the manifold. As an example, we illustrate this type of quanitzation of the torus. We exhibit Berezin-Toeplitz quantization of a complex manifold in the same spirit as above.
