Quantum Monads in Phase Space and Related Toeplitz Operators
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909894341296128 |
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| author | de Gosson, Maurice |
| author_facet | de Gosson, Maurice |
| contents | In earlier work, we introduced quantum blobs as minimum-uncertainty symplectic ellipsoids in phase space. These objects may be viewed as geometric monads in the Leibnizian sense, representing the elementary units of phase-space structure consistent with the uncertainty principle. We establish a one-to-one correspondence between such monads and generalized coherent states, represented by arbitrary non-degenerate Gaussian wave functions in configuration space. To each of these states, we associate a classs of Toeplitz operators that extends the standard anti-Wick quantization scheme. The mathematical and physical properties of these operators are analyzed, allowing for a generalized definition of density matrices within the phase-space formulation of quantum mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06491 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Monads in Phase Space and Related Toeplitz Operators de Gosson, Maurice Quantum Physics Mathematical Physics In earlier work, we introduced quantum blobs as minimum-uncertainty symplectic ellipsoids in phase space. These objects may be viewed as geometric monads in the Leibnizian sense, representing the elementary units of phase-space structure consistent with the uncertainty principle. We establish a one-to-one correspondence between such monads and generalized coherent states, represented by arbitrary non-degenerate Gaussian wave functions in configuration space. To each of these states, we associate a classs of Toeplitz operators that extends the standard anti-Wick quantization scheme. The mathematical and physical properties of these operators are analyzed, allowing for a generalized definition of density matrices within the phase-space formulation of quantum mechanics. |
| title | Quantum Monads in Phase Space and Related Toeplitz Operators |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2511.06491 |