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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.04865 |
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| _version_ | 1866914448961175552 |
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| author | Combe, N. C. Combe, P. G. Nencka, H. K. |
| author_facet | Combe, N. C. Combe, P. G. Nencka, H. K. |
| contents | We introduce the Legendre bundle, a geometric structure encoding the essential duality of dually flat (Hessian) manifolds, and demonstrate that both exponential families in information geometry and a natural class of quantum field theories -- which we term Hessian QFTs -- arise as distinct realisations of this single framework. The Legendre bundle is shown to carry a canonical para-Kähler structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04865 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Duality, Legendre Bundles and Deformations Combe, N. C. Combe, P. G. Nencka, H. K. Differential Geometry We introduce the Legendre bundle, a geometric structure encoding the essential duality of dually flat (Hessian) manifolds, and demonstrate that both exponential families in information geometry and a natural class of quantum field theories -- which we term Hessian QFTs -- arise as distinct realisations of this single framework. The Legendre bundle is shown to carry a canonical para-Kähler structure. |
| title | On Duality, Legendre Bundles and Deformations |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.04865 |