On the geometric quantization of $θ$-almost twisted Poisson manifold
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911176195047424 |
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| author | Nansidi, Nasser Saipele Ndawa, Bertuel Tangue Dongho, Joseph |
| author_facet | Nansidi, Nasser Saipele Ndawa, Bertuel Tangue Dongho, Joseph |
| contents | A $θ$-almost twisted Poisson manifold is a manifold $M$ together with a bivector field $Λ$, a 3-form $φ$, and a closed 1-form $θ$ such that the exterior derivative $dφ$ of $φ$ is the wedge product of $θ$ and $φ$, the anchor $Λ^\#(θ)$ of $θ$ is identically zero, and the Jacobiator (Jacobi operator; which is half the Schouten-Nijenhuis bracket of $Λ$ with itself) associated to $Λ$ is the anchor $Λ^\#(φ)$ of $φ$. In this work, we define the notion of a contravariant derivative adapted to these manifolds and establish the prequantization condition in terms of the $θ$-almost twisted Poisson cohomology. We then introduce a polarization and construct a quantum Hilbert space. These results are illustrated by examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the geometric quantization of $θ$-almost twisted Poisson manifold Nansidi, Nasser Saipele Ndawa, Bertuel Tangue Dongho, Joseph Dynamical Systems A $θ$-almost twisted Poisson manifold is a manifold $M$ together with a bivector field $Λ$, a 3-form $φ$, and a closed 1-form $θ$ such that the exterior derivative $dφ$ of $φ$ is the wedge product of $θ$ and $φ$, the anchor $Λ^\#(θ)$ of $θ$ is identically zero, and the Jacobiator (Jacobi operator; which is half the Schouten-Nijenhuis bracket of $Λ$ with itself) associated to $Λ$ is the anchor $Λ^\#(φ)$ of $φ$. In this work, we define the notion of a contravariant derivative adapted to these manifolds and establish the prequantization condition in terms of the $θ$-almost twisted Poisson cohomology. We then introduce a polarization and construct a quantum Hilbert space. These results are illustrated by examples. |
| title | On the geometric quantization of $θ$-almost twisted Poisson manifold |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2509.21168 |