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2017 Geometric Quantization of Finite Toda Systems and Coherent States
Rukmini Dey, Saibal Ganguli
J. Geom. Symmetry Phys. 44: 21-38 (2017). DOI: 10.7546/jgsp-44-2017-21-38

Abstract

Adler had showed that the Toda system can be given a coadjoint orbit description. We quantize the Toda system by viewing it as a single orbit of a multiplicative group of lower triangular matrices of determinant one with positive diagonal entries. We get a unitary representation of the group with square integrable polarized sections of the quantization as the module. We find the Rawnsley coherent states after completion of the above space of sections. We also find non-unitary finite dimensional quantum Hilbert spaces for the system. Finally we give an expression for the quantum Hamiltonian for the system.

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Rukmini Dey. Saibal Ganguli. "Geometric Quantization of Finite Toda Systems and Coherent States." J. Geom. Symmetry Phys. 44 21 - 38, 2017. https://doi.org/10.7546/jgsp-44-2017-21-38

Information

Published: 2017
First available in Project Euclid: 6 July 2017

zbMATH: 06810364
MathSciNet: MR3700455
Digital Object Identifier: 10.7546/jgsp-44-2017-21-38

Rights: Copyright © 2017 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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