One shows that the Feynman’s Path Integral designed for quantum mechanics has an analogous in classical mechanics, the so-called (min, +) Path Integral. This former is build on (min, +)-algebra and (min, +)-analysis which permit to handle in a linear way non-linear problems occurring in mathematical physics. The Hamilton-Jacobi equations and their solutions within this mathematical framework, are introduced and yield to a new interpretation expressed in a duality between action field and particle.

中文翻译：

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（min，+）路径积分和动作粒子对偶的半经典极限和最小动作原理

一个表明，为量子力学设计的费曼路径积分与经典力学类似，即所谓的（最小，+）路径积分。前者是建立在（min，+）-代数和（min，+）-分析的基础上的，它们允许以线性方式处理数学物理学中出现的非线性问题。引入了Hamilton-Jacobi方程及其在该数学框架内的解，并给出了以作用场与粒子之间的对偶表示的新解释。