Universality of the Weyl-Heisenberg symmetry and its covariant quantisations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929639619821568 |
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| author | Gazeau, Jean-Pierre Habonimana, Célestin Murenzi, Romain Zlotak, Aidan |
| author_facet | Gazeau, Jean-Pierre Habonimana, Célestin Murenzi, Romain Zlotak, Aidan |
| contents | The Weyl-Heisenberg symmetries originate from translation invariances of various manifolds viewed as phase spaces, e.g. Euclidean plane, semi-discrete cylinder, torus, in the two-dimensional case, and higher-dimensional generalisations. In this review we describe, on an elementary level, how this symmetry emerges through displacement operators and standard Fourier analysis, and how their unitary representations are used both in Signal Analysis (time-frequency techniques, Gabor transform) and in quantum formalism (covariant integral quantizations and semi-classical portraits). An example of application of the formalism to the Majorana stellar constellation in the plane is presented. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_14227 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universality of the Weyl-Heisenberg symmetry and its covariant quantisations Gazeau, Jean-Pierre Habonimana, Célestin Murenzi, Romain Zlotak, Aidan Quantum Physics 81R05, 81R30, 81S10, 81S30, 81P16 The Weyl-Heisenberg symmetries originate from translation invariances of various manifolds viewed as phase spaces, e.g. Euclidean plane, semi-discrete cylinder, torus, in the two-dimensional case, and higher-dimensional generalisations. In this review we describe, on an elementary level, how this symmetry emerges through displacement operators and standard Fourier analysis, and how their unitary representations are used both in Signal Analysis (time-frequency techniques, Gabor transform) and in quantum formalism (covariant integral quantizations and semi-classical portraits). An example of application of the formalism to the Majorana stellar constellation in the plane is presented. |
| title | Universality of the Weyl-Heisenberg symmetry and its covariant quantisations |
| topic | Quantum Physics 81R05, 81R30, 81S10, 81S30, 81P16 |
| url | https://arxiv.org/abs/2412.14227 |