TY - JOUR
T1 - Generalized Berezin quantization, Bergman metrics and fuzzy Laplacians
AU - Iuliu Lazaroiu, Calin
AU - McNamee, Daniel
AU - Saemann, Christian
N1 - 65+1 pages, JHEP style, version to appear in JHEP
PY - 2008/4/29
Y1 - 2008/4/29
N2 - 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.
AB - 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.
U2 - 10.1088/1126-6708/2008/09/059
DO - 10.1088/1126-6708/2008/09/059
M3 - Article
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
ER -