Saez Diaz, Pedro (2026) Squeezed States and the Role of the Metaplectic Group Mp(2n,R). Bachelor's Thesis, Mathematics.
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Abstract
This thesis addresses the question of how (squeezed) coherent states and phase space distributions transform under the symmetries of phase space. This will require a detailed study of the unitary representations of the metaplectic and the Jacobi group. It is shown that the Schrödinger representation of the Heisenberg group and the Weil representation of the metaplectic group can be combined to describe how canonical coherent states transform under displacements in phase space and linear canonical transformations. Under this formalism, it is proved that the set of squeezed coherent states remains closed under both of these operations. This report concludes with a description of the Feichtinger algebra and its relationship with the metaplectic group and the Wigner distribution that can be extended to more general quantum states.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Boer, D. and Waalkens, H. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 06 May 2026 11:33 |
| Last Modified: | 06 May 2026 11:33 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37303 |
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