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Twisted Fock representations of noncommutative Kähler manifolds

Autor(en)
Akifumi Sako, Hiroshi Umetsu
Abstrakt

We introduce twisted Fock representations of noncommutative Kähler manifolds and give their explicit expressions. The twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by applying creation operators to a vacuum state. "Twisted" means that creation operators are not Hermitian conjugate of annihilation operators in this representation. In deformation quantization of Kähler manifolds with separation of variables formulated by Karabegov, local complex coordinates and partial derivatives of the Kähler potential with respect to coordinates satisfy the commutation relations between the creation and annihilation operators. Based on these relations, we construct the twisted Fock representation of noncommutative Kähler manifolds and give a dictionary to translate between the twisted Fock representations and functions on noncommutative Kähler manifolds concretely.

Organisation(en)
Mathematische Physik
Externe Organisation(en)
Tokyo University of Science, Universität Wien, National Institute of Technology, Ishikawa College
Journal
Journal of Mathematical Physics
Band
57
Anzahl der Seiten
20
ISSN
0022-2488
DOI
https://doi.org/10.1063/1.4961930
Publikationsdatum
09-2016
Peer-reviewed
Ja
ÖFOS 2012
103036 Theoretische Physik, 103019 Mathematische Physik
Schlagwörter
ASJC Scopus Sachgebiete
Statistical and Nonlinear Physics, Mathematical Physics
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/0832f752-e5c5-455a-aef2-67892340b9a0