Some basics of su(1,1)
A basic introduction to the su(1,1) algebra is presented, in which we discuss the relation with canonical transformations, the realization in terms of quantized radiation field modes and coherent states. Instead of going into details of these topics, we rather emphasize the existing connections betw...
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Sociedade Brasileira de Física
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| Series: | Revista Brasileira de Ensino de Física |
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| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172004000400008&lng=en&tlng=en |
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doaj-241c024877274dae8c8c07d1ceabea452020-11-25T03:38:26ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-11171806-912626435135710.1590/S1806-11172004000400008S1806-11172004000400008Some basics of su(1,1)Marcel Novaes0Universidade Estadual de CampinasA basic introduction to the su(1,1) algebra is presented, in which we discuss the relation with canonical transformations, the realization in terms of quantized radiation field modes and coherent states. Instead of going into details of these topics, we rather emphasize the existing connections between them. We discuss two parametrizations of the coherent states manifold SU(1,1)/U(1): as the Poincaré disk in the complex plane and as the pseudosphere (a sphere in a Minkowskian space), and show that it is a natural phase space for quantum systems with SU(1,1) symmetry.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172004000400008&lng=en&tlng=ensu(1,1) algebrasu(1,1) groupcanonical transformationscoherent statessecond quantizationpseudosphere |
| collection |
DOAJ |
| language |
Portuguese |
| format |
Article |
| sources |
DOAJ |
| author |
Marcel Novaes |
| spellingShingle |
Marcel Novaes Some basics of su(1,1) Revista Brasileira de Ensino de Física su(1,1) algebra su(1,1) group canonical transformations coherent states second quantization pseudosphere |
| author_facet |
Marcel Novaes |
| author_sort |
Marcel Novaes |
| title |
Some basics of su(1,1) |
| title_short |
Some basics of su(1,1) |
| title_full |
Some basics of su(1,1) |
| title_fullStr |
Some basics of su(1,1) |
| title_full_unstemmed |
Some basics of su(1,1) |
| title_sort |
some basics of su(1,1) |
| publisher |
Sociedade Brasileira de Física |
| series |
Revista Brasileira de Ensino de Física |
| issn |
1806-1117 1806-9126 |
| description |
A basic introduction to the su(1,1) algebra is presented, in which we discuss the relation with canonical transformations, the realization in terms of quantized radiation field modes and coherent states. Instead of going into details of these topics, we rather emphasize the existing connections between them. We discuss two parametrizations of the coherent states manifold SU(1,1)/U(1): as the Poincaré disk in the complex plane and as the pseudosphere (a sphere in a Minkowskian space), and show that it is a natural phase space for quantum systems with SU(1,1) symmetry. |
| topic |
su(1,1) algebra su(1,1) group canonical transformations coherent states second quantization pseudosphere |
| url |
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172004000400008&lng=en&tlng=en |
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AT marcelnovaes somebasicsofsu11 |
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