Title:	Coadjoint orbits and Kähler Structure: Examples from Coherent States
Authors:	Dey, Rukmini Samuel, J. Vidyarthi, Rithwik S.
Keywords:	coherent states squeezed states coadjoint orbits Toda system
Issue Date:	1-Jun-2022
Publisher:	Elsevier
Citation:	Reports on Mathematical Physics, 2022, Vol.89, p267
Abstract:	Do co-adjoint orbits of Lie groups support a Kähler structure? We study this question from a point of view derived from coherent states. We examine three examples of Lie groups: the Weyl–Heisenberg group, SU(2) and SU(1, 1). In cases, where the orbits admit a Kähler structure, we show that coherent states give us a Kähler embedding of the orbit into projective Hilbert space. In contrast, squeezed states (which like coherent states, also saturate the uncertainty bound) only give us a symplectic embedding. We also study geometric quantisation of the co-adjoint orbits of the group SUT(2, ℝ) of real, special, upper triangular matrices in two dimensions. We glean some general insights from these examples. Our presentation is semi-expository and accessible to physicists.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/7985
ISSN:	0034-4877
Alternative Location:	https://arxiv.org/abs/2105.14283 https://doi.org/10.1016/S0034-4877(22)00033-7 https://ui.adsabs.harvard.edu/abs/2021arXiv210514283D/abstract
Copyright:	2022 Elsevier B.V.
Appears in Collections:	Research Papers (TP)

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