Generalized Berezin quantization, Bergman metrics and fuzzy Laplacians

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Lazaroiu, Calin Iuliu
McNamee, Daniel
Saemann, Christian
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Abstract
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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.
Comment: 65+1 pages, JHEP style, version to appear in JHEP
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High Energy Physics - Theory
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