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

Martin Bordemann; Eckhard Meinrenken; Martin Schlichenmaier

doi:10.1007/bf02099772

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arXiv · hep-th/9309134

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

Martin Bordemann·Eckhard Meinrenken·Martin Schlichenmaier

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Abstract

For general compact Kähler 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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Martin Bordemann, Eckhard Meinrenken, Martin Schlichenmaier. 1994-05-26. Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to\infty$. https://doi.org/10.1007/bf02099772

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