On a Quantization of the Classical θ-Functions

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2015
• Main Author: Brezhnev, Y.V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147012
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On a Quantization of the Classical θ-Functions / Y.V. Brezhnev // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 19 назв. — англ.

The Jacobi theta-functions admit a definition through the autonomous differential equations (dynamical system); not only through the famous Fourier theta-series. We study this system in the framework of Hamiltonian dynamics and find corresponding Poisson brackets. Availability of these ingredients a...