标题： 自然理论 显示英文标题

标题： Natural Theories

摘要： 我们考虑由自然方程给出动力学的物理理论类，这些自然方程是由从n流形范畴（对于某个n）到纤维丛范畴的函子确定的偏微分方程，满足某些进一步条件。 我们展示了自然方程理论如何澄清几个重要的基础问题，包括最小耦合的地位和意义、理论的对称性以及背景结构。 我们还陈述并证明了关于自然方程初值问题的一个基本结果。 显示英文摘要

摘要： We consider the class of physical theories whose dynamics are given by natural equations, which are partial differential equations determined by a functor from the category of n-manifolds, for some n, to the category of fiber bundles, satisfying certain further conditions. We show how the theory of natural equations clarifies several important foundational issues, including the status and meaning of minimal coupling, symmetries of theories, and background structure. We also state and prove a fundamental result about the initial value problem for natural equations.