dorsal/arxiv
View SchemaDecomposition of Hilbert space in sets of coherent states
| Authors | Nuno Barros e Sa |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0009022 |
| URL | https://arxiv.org/abs/quant-ph/0009022 |
| DOI | 10.1088/0305-4470/34/23/304 |
| Journal | J.Phys.A: Math.Gen. 34 (2001) 4831 |
Abstract
Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups. The group SU(2) is studied in particular and the orbit spaces of its j=1/2 and j=1 representations completely determined. The orbits of SU(2) in CP^N can be either 2 or 3 dimensional, the first of them being either isomorphic to S^2 or to RP^2 and the latter being isomorphic to quotient spaces of RP^3. We end with a look from the same perspective to the quantum mechanical space of states in particle mechanics.
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"abstract": "Within the generalized definition of coherent states as group orbits we study\nthe orbit spaces and the orbit manifolds in the projective spaces constructed\nfrom linear representations. Invariant functions are suggested for arbitrary\ngroups. The group SU(2) is studied in particular and the orbit spaces of its\nj=1/2 and j=1 representations completely determined. The orbits of SU(2) in\nCP^N can be either 2 or 3 dimensional, the first of them being either\nisomorphic to S^2 or to RP^2 and the latter being isomorphic to quotient spaces\nof RP^3. We end with a look from the same perspective to the quantum mechanical\nspace of states in particle mechanics.",
"arxiv_id": "quant-ph/0009022",
"authors": [
"Nuno Barros e Sa"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/34/23/304",
"journal_ref": "J.Phys.A: Math.Gen. 34 (2001) 4831",
"title": "Decomposition of Hilbert space in sets of coherent states",
"url": "https://arxiv.org/abs/quant-ph/0009022"
},
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