Generalized Berezin quantization, Bergman metrics and fuzzy Laplacians

Details Generalized Berezin quantization, Bergman metrics and fuzzy Laplacians Generalized Berezin quantization, Bergman metrics and fuzzy Laplacians

2008-04-29

arxiv.org/abs/0804.4555v2

JHEP 0809:059,2008

Physics

High Energy Physics

High Energy Physics - Theory

65+1 pages, JHEP style, version to appear in JHEP

Scientific paper

10.1088/1126-6708/2008/09/059

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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