Geometric quantization of finite Toda systems and coherent States
Differential Geometry
2017-04-18 v3 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
Adler had shown in 1979 that the Toda system can be given a coad- joint 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 pos- itive 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 a completion of the above space of sections. We also find non-unitary finite dimensional quantum Hilbert spaces for the system.
Keywords
Cite
@article{arxiv.1612.02987,
title = {Geometric quantization of finite Toda systems and coherent States},
author = {Rukmini Dey and Saibal Ganguli},
journal= {arXiv preprint arXiv:1612.02987},
year = {2017}
}
Comments
Section on coherent states extended with detailed description of evaluativeness. Quantum Hamiltonian found and the statement on spectrum revoked