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Bibliographic Details
Main Authors:	Combe, N. C., Combe, P. G., Nencka, H. K.
Format:	Preprint
Published:	2026
Subjects:	Differential Geometry
Online Access:	https://arxiv.org/abs/2604.04865
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Table of 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.