A Phase Space Representation of the Metaplectic Group
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909972486422528 |
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| author | de Gosson, Maurice |
| author_facet | de Gosson, Maurice |
| contents | The symplectic group Sp(n) acts on phase space while the unitary representation of its double cover, Mp(n), the metaplectic group, acts on functions defined on configuration space. We will construct an extension Mp(n) of Mp(n) acting on square integrable functions on phase space. This is performed using previous results of ours involving explicit expressions of the twisted Weyl symbols of metaplectic operators and Bopp pseudodifferential operators, which are phase space extensions of the usual Weyl operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18415 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Phase Space Representation of the Metaplectic Group de Gosson, Maurice Mathematical Physics Analysis of PDEs Symplectic Geometry Quantum Physics The symplectic group Sp(n) acts on phase space while the unitary representation of its double cover, Mp(n), the metaplectic group, acts on functions defined on configuration space. We will construct an extension Mp(n) of Mp(n) acting on square integrable functions on phase space. This is performed using previous results of ours involving explicit expressions of the twisted Weyl symbols of metaplectic operators and Bopp pseudodifferential operators, which are phase space extensions of the usual Weyl operators. |
| title | A Phase Space Representation of the Metaplectic Group |
| topic | Mathematical Physics Analysis of PDEs Symplectic Geometry Quantum Physics |
| url | https://arxiv.org/abs/2512.18415 |