Proceedings of the International Conference on Geometry, Integrability and Quantization

Deformation Quantization of Kähler Manifolds and Their Twisted Fock Representation

Akifumi Sako and Hiroshi Umetsu

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Abstract

We introduce the notion of twisted Fock representations of noncommutative Kähler manifolds and give their explicit expressions. The so-called twisted Fock representation is a representation of the Heisenberg like algebra whose states are constructed by acting creation operators on a vacuum state. “Twisted” means that creation operators are not Hermitian conjugate of annihilation operators. 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, the twisted Fock representation of noncommutative Kähler manifolds is constructed.

Article information

Source
Proceedings of the Eighteenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Guowu Meng and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2017), 225-240

Dates
First available in Project Euclid: 14 January 2017

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1484362827

Digital Object Identifier
doi:10.7546/giq-18-2017-225-240

Mathematical Reviews number (MathSciNet)
MR3616924

Zentralblatt MATH identifier
1385.53082

Citation

Sako, Akifumi; Umetsu, Hiroshi. Deformation Quantization of Kähler Manifolds and Their Twisted Fock Representation. Proceedings of the Eighteenth International Conference on Geometry, Integrability and Quantization, 225--240, Avangard Prima, Sofia, Bulgaria, 2017. doi:10.7546/giq-18-2017-225-240. https://projecteuclid.org/euclid.pgiq/1484362827


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