Generalized coherent states and the diagonal representation for operators

Mukunda, N. ; Arvind, ; Chaturvedi, S. ; Simon, R. (2003) Generalized coherent states and the diagonal representation for operators Journal of Mathematical Physics, 44 (6). pp. 2479-2506. ISSN 0022-2488

[img]
Preview
PDF - Publisher Version
314kB

Official URL: http://jmp.aip.org/resource/1/jmapaq/v44/i6/p2479_...

Related URL: http://dx.doi.org/10.1063/1.1559416

Abstract

We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with a 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 theorem associated with induced unitary group representations. Applications to several examples involving SU(2), SU(3), 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.

Item Type:Article
Source:Copyright of this article belongs to American Institute of Physics.
ID Code:25325
Deposited On:06 Dec 2010 13:34
Last Modified:17 May 2016 08:49

Repository Staff Only: item control page