Frames, the beta-duality in Minkowski space and spin coherent states
In the spirit of some earlier work on building coherent states for the Poincaré group in one space and one time dimension, we construct here analogous families of states for the full Poincaré group, for representations corresponding to mass m > 0 and arbitrary integral or half-integral spin. Ea...
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| Format: | Article |
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1996
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| author | Ali, S.T. Gazeau, J.P. Karim, M.R. |
| author_facet | Ali, S.T. Gazeau, J.P. Karim, M.R. |
| author_sort | Ali, S.T. |
| collection | UM |
| description | In the spirit of some earlier work on building coherent states for the Poincaré group in one space and one time dimension, we construct here analogous families of states for the full Poincaré group, for representations corresponding to mass m > 0 and arbitrary integral or half-integral spin. Each family of coherent states is defined by an affine section in the group and constitutes a frame. The sections, in their turn, are determined by particular velocity vector fields, the latter always appearing in dual pairs. Geometrically, each family of coherent states is related to the choice of a Riemannian structure on the forward mass hyperboloid or, equivalently, to the choice of a certain parallel bundle in the relativistic phase space. The large variety of coherent states obtained tempts us to believe that there is rich scope here for application to spin-dependent problems in atomic and nuclear physics, as well as to image reconstruction problems, using the discretized versions of these frames. © 1996 IOP Publishing Ltd. |
| first_indexed | 2024-03-06T05:22:02Z |
| format | Article |
| id | um.eprints-8756 |
| institution | Universiti Malaya |
| last_indexed | 2024-03-06T05:22:02Z |
| publishDate | 1996 |
| record_format | dspace |
| spelling | um.eprints-87562014-01-02T07:04:22Z http://eprints.um.edu.my/8756/ Frames, the beta-duality in Minkowski space and spin coherent states Ali, S.T. Gazeau, J.P. Karim, M.R. TA Engineering (General). Civil engineering (General) In the spirit of some earlier work on building coherent states for the Poincaré group in one space and one time dimension, we construct here analogous families of states for the full Poincaré group, for representations corresponding to mass m > 0 and arbitrary integral or half-integral spin. Each family of coherent states is defined by an affine section in the group and constitutes a frame. The sections, in their turn, are determined by particular velocity vector fields, the latter always appearing in dual pairs. Geometrically, each family of coherent states is related to the choice of a Riemannian structure on the forward mass hyperboloid or, equivalently, to the choice of a certain parallel bundle in the relativistic phase space. The large variety of coherent states obtained tempts us to believe that there is rich scope here for application to spin-dependent problems in atomic and nuclear physics, as well as to image reconstruction problems, using the discretized versions of these frames. © 1996 IOP Publishing Ltd. 1996-09-07 Article PeerReviewed Ali, S.T. and Gazeau, J.P. and Karim, M.R. (1996) Frames, the beta-duality in Minkowski space and spin coherent states. Journal of Physics a-Mathematical and General, 29 (17). pp. 5529-5549. ISSN 0305-4470, DOI https://doi.org/10.1088/0305-4470/29/17/024 <https://doi.org/10.1088/0305-4470/29/17/024>. http://www.scopus.com/inward/record.url?eid=2-s2.0-0038606703&partnerID=40&md5=6a79b0276667f5a5606ec5ce0d59a490 http://iopscience.iop.org/0305-4470/29/17/024 Doi 10.1088/0305-4470/29/17/024 |
| spellingShingle | TA Engineering (General). Civil engineering (General) Ali, S.T. Gazeau, J.P. Karim, M.R. Frames, the beta-duality in Minkowski space and spin coherent states |
| title | Frames, the beta-duality in Minkowski space and spin coherent states |
| title_full | Frames, the beta-duality in Minkowski space and spin coherent states |
| title_fullStr | Frames, the beta-duality in Minkowski space and spin coherent states |
| title_full_unstemmed | Frames, the beta-duality in Minkowski space and spin coherent states |
| title_short | Frames, the beta-duality in Minkowski space and spin coherent states |
| title_sort | frames the beta duality in minkowski space and spin coherent states |
| topic | TA Engineering (General). Civil engineering (General) |
| work_keys_str_mv | AT alist framesthebetadualityinminkowskispaceandspincoherentstates AT gazeaujp framesthebetadualityinminkowskispaceandspincoherentstates AT karimmr framesthebetadualityinminkowskispaceandspincoherentstates |