Generalized Heisenberg-Weyl groups and Hermite functions
A generalisation of Euclidean and pseudo-Euclidean groups is presented, where the Weyl-Heisenberg groups, well known in quantum mechanics, are involved. A new family of groups is obtained including all the above-mentioned groups as subgroups. Symmetries, like self-similarity and invariance with resp...
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| Format: | Article |
| Language: | English |
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SciPost
2023-11-01
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| Series: | SciPost Physics Proceedings |
| Online Access: | https://scipost.org/SciPostPhysProc.14.023 |
| _version_ | 1797483326421860352 |
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| author | Enrico Celeghini, Manuel Gadella, Mariano A. del Olmo |
| author_facet | Enrico Celeghini, Manuel Gadella, Mariano A. del Olmo |
| author_sort | Enrico Celeghini, Manuel Gadella, Mariano A. del Olmo |
| collection | DOAJ |
| description | A generalisation of Euclidean and pseudo-Euclidean groups is presented, where the Weyl-Heisenberg groups, well known in quantum mechanics, are involved. A new family of groups is obtained including all the above-mentioned groups as subgroups. Symmetries, like self-similarity and invariance with respect to the orientation of the axes, are properly included in the structure of this new family of groups. Generalized Hermite functions on multidimensional spaces, which serve as orthogonal bases of Hilbert spaces supporting unitary irreducible representations of these new groups, are introduced. |
| first_indexed | 2024-03-09T22:46:20Z |
| format | Article |
| id | doaj.art-4b710c8445a34406b2089650449d3dd1 |
| institution | Directory Open Access Journal |
| issn | 2666-4003 |
| language | English |
| last_indexed | 2024-03-09T22:46:20Z |
| publishDate | 2023-11-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics Proceedings |
| spelling | doaj.art-4b710c8445a34406b2089650449d3dd12023-11-23T18:28:39ZengSciPostSciPost Physics Proceedings2666-40032023-11-011402310.21468/SciPostPhysProc.14.023Generalized Heisenberg-Weyl groups and Hermite functionsEnrico Celeghini, Manuel Gadella, Mariano A. del OlmoA generalisation of Euclidean and pseudo-Euclidean groups is presented, where the Weyl-Heisenberg groups, well known in quantum mechanics, are involved. A new family of groups is obtained including all the above-mentioned groups as subgroups. Symmetries, like self-similarity and invariance with respect to the orientation of the axes, are properly included in the structure of this new family of groups. Generalized Hermite functions on multidimensional spaces, which serve as orthogonal bases of Hilbert spaces supporting unitary irreducible representations of these new groups, are introduced.https://scipost.org/SciPostPhysProc.14.023 |
| spellingShingle | Enrico Celeghini, Manuel Gadella, Mariano A. del Olmo Generalized Heisenberg-Weyl groups and Hermite functions SciPost Physics Proceedings |
| title | Generalized Heisenberg-Weyl groups and Hermite functions |
| title_full | Generalized Heisenberg-Weyl groups and Hermite functions |
| title_fullStr | Generalized Heisenberg-Weyl groups and Hermite functions |
| title_full_unstemmed | Generalized Heisenberg-Weyl groups and Hermite functions |
| title_short | Generalized Heisenberg-Weyl groups and Hermite functions |
| title_sort | generalized heisenberg weyl groups and hermite functions |
| url | https://scipost.org/SciPostPhysProc.14.023 |
| work_keys_str_mv | AT enricoceleghinimanuelgadellamarianoadelolmo generalizedheisenbergweylgroupsandhermitefunctions |