Generalized Berezin quantization, Bergman metrics and fuzzy Laplacians
High Energy Physics - Theory
2009-12-10 v2
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.
Cite
@article{arxiv.0804.4555,
title = {Generalized Berezin quantization, Bergman metrics and fuzzy Laplacians},
author = {Calin Iuliu Lazaroiu and Daniel McNamee and Christian Saemann},
journal= {arXiv preprint arXiv:0804.4555},
year = {2009}
}
Comments
65+1 pages, JHEP style, version to appear in JHEP