Geometric quantization of finite Toda systems and coherent States [article]

Rukmini Dey, Saibal Ganguli
2017 arXiv   pre-print
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
more » ... e dimensional quantum Hilbert spaces for the system.
arXiv:1612.02987v3 fatcat:dzxm4sv4vbcfbbpyfnlis5m62q