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Generalized coherent states and the diagonal representation for operators

Mukunda, N and Arvind, * and Chaturvedi, S and Simon, R (2003) Generalized coherent states and the diagonal representation for operators. In: Journal of Mathematical Physics, 44 (6). pp. 2479-506.


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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: Journal Article
Publication: Journal of Mathematical Physics
Publisher: American Institute of Physics (AIP)
Additional Information: The DOI is currently only displayed. Copyright for this article belongs to American Institute of Physics (AIP)
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies (Ceased to exist at the end of 2003)
Date Deposited: 09 Jun 2004
Last Modified: 19 Sep 2010 04:12
URI: http://eprints.iisc.ac.in/id/eprint/241

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