|
| related topics |
| {group, space, representation} |
| {states, state, optimal} |
| {let, theorem, proof} |
| {state, states, coherent} |
| {operator, operators, space} |
| {equation, function, exp} |
| {vol, operators, histories} |
| {energy, gaussian, time} |
|
Generalised coherent states and the diagonal representation for operators
N. Mukunda, S. Arvind, R. Chaturvedi
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 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 $SU(2),$ $SU(3),$ 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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0002070
- categories:
- quant-ph
- comments:
- (24 pages, no figures)
- arxiv_id:
- quant-ph/0002070
- created:
- 2000-02-24
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