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arXiv · 0804.4555

Generalized Berezin quantization, Bergman metrics and fuzzy Laplacians

Calin Iuliu Lazaroiu·Daniel McNamee·Christian Saemann
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Abstract

We study extended Berezin and Berezin-Toeplitz quantization for compact Kaehler manifolds, two related quantization procedures which provide a general framework for approaching the construction of fuzzy compact Kaehler geometries. Using this framework, we show that a particular version of generalized Berezin quantization, which we baptize "Berezin-Bergman quantization", reproduces recent proposals for the construction of fuzzy Kaehler spaces. We also discuss how fuzzy Laplacians can be defined in our general framework and study a few explicit examples. Finally, we use this approach to propose a general explicit definition of fuzzy scalar field theory on compact Kaehler manifolds.

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Calin Iuliu Lazaroiu, Daniel McNamee, Christian Saemann. 2008-09-09. Generalized Berezin quantization, Bergman metrics and fuzzy Laplacians. https://doi.org/10.1088/1126-6708%2F2008%2F09%2F059

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