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.
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|
|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|
|Date Deposited:||09 Jun 2004|
|Last Modified:||19 Sep 2010 04:12|
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