Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to\infty$

Details Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to\infty$ Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to\infty$

1993-09-24

arxiv.org/abs/hep-th/9309134v3

Commun.Math.Phys. 165 (1994) 281-296

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, AmsTeX 2.1, Sept. 93 (rev: only typos are corrected)

Scientific paper

10.1007/BF02099772

For general compact K\"ahler manifolds it is shown that both Toeplitz quantization and geometric quantization lead to a well-defined (by operator norm estimates) classical limit. This generalizes earlier results of the authors and Klimek and Lesniewski obtained for the torus and higher genus Riemann surfaces, respectively. We thereby arrive at an approximation of the Poisson algebra by a sequence of finite-dimensional matrix algebras $gl(N)$, $N\to\infty$.

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