Non-Symplectic Deformations of Geometric Quantisation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908670983405568 |
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| author | Maxwell, Kerr |
| author_facet | Maxwell, Kerr |
| contents | We introduce the notion of geometric pseudo-quantisation based on geometric quantisation with a weakened curvature condition. We show how such a structure arises naturally from simple deformations of the symplectic structure and pullbacks of prequantum data by non-symplectic diffeomorphisms. Our main result is deriving the equations of motion for some simple pseudo-quantisations. We also compute the pseudo-quantisation of several simple examples from symplectic and almost-symplectic geometry, as well as the general form of the resulting deformed canonical commutator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18549 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Symplectic Deformations of Geometric Quantisation Maxwell, Kerr Mathematical Physics Symplectic Geometry 53D50, 81S10 We introduce the notion of geometric pseudo-quantisation based on geometric quantisation with a weakened curvature condition. We show how such a structure arises naturally from simple deformations of the symplectic structure and pullbacks of prequantum data by non-symplectic diffeomorphisms. Our main result is deriving the equations of motion for some simple pseudo-quantisations. We also compute the pseudo-quantisation of several simple examples from symplectic and almost-symplectic geometry, as well as the general form of the resulting deformed canonical commutator. |
| title | Non-Symplectic Deformations of Geometric Quantisation |
| topic | Mathematical Physics Symplectic Geometry 53D50, 81S10 |
| url | https://arxiv.org/abs/2511.18549 |