Generalised coherent states and the diagonal representation for operators
摘要
We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with an unitary irreducible representation of a (compact) Lie group. We show that necessary and sufficient conditions for the possibility of such a representation can be obtained by combining Clebsch-Gordan theory and the reciprocity theorems associated with induced unitary group representation. Applications to several examples involving and the Heisenberg-Weyl group are presented, showing that there are simple examples of generalized coherent states which do not meet these conditions. Our results are relevant for phase-space description of quantum mechanics and quantum state reconstruction problems.
引用
@article{arxiv.quant-ph/0002070,
title = {Generalised coherent states and the diagonal representation for operators},
author = {N. Mukunda and Arvind and S. Chaturvedi and R. Simon},
journal= {arXiv preprint arXiv:quant-ph/0002070},
year = {2018}
}
备注
(24 pages, no figures)