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