The theory of $F$‐manifolds, and more generally, manifolds endowed with commutative and associative multiplication of their tangent fields, was discovered and formalised in various models of quantum field theory involving algebraic and analytic geometry, at least since the 1990s.

中文翻译：

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F流形和信息几何

的理论 $F$至少从1990年代开始，在涉及代数和解析几何的各种量子场理论模型中发现并形式化了流形，并且更普遍地讲，流形具有正切场的可交换和缔合乘法。