标题： 希尔伯特流形上的量子力学：功能相对性原理 显示英文标题

标题： Quantum mechanics on Hilbert manifolds: The principle of functional relativity

摘要： 量子力学被表述为在希尔伯特流形上的几何理论。流形上坐标图的图像被允许属于任意的函数希尔伯特空间，包括广义函数空间。在这种情况下，张量方程也被称为泛函张量方程，它们描述了在各种函数希尔伯特空间上的泛函方程族。引入了泛函相对性原理，该原理指出量子理论确实是一种泛函张量理论，即它可以通过泛函张量方程来描述。量子理论的主要方程被证明与泛函相对性原理相容。通过接受该原理作为假设，我们随后分析了物理维度的起源，提供了普朗克常数的几何解释，并找到了双缝实验和测量过程的简单解释。 显示英文摘要

摘要： Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this setting, also called functional tensor equations, describe families of functional equations on various Hilbert spaces of functions. The principle of functional relativity is introduced which states that quantum theory is indeed a functional tensor theory, i.e., it can be described by functional tensor equations. The main equations of quantum theory are shown to be compatible with the principle of functional relativity. By accepting the principle as a hypothesis, we then analyze the origin of physical dimensions, provide a geometric interpretation of Planck's constant, and find a simple interpretation of the two-slit experiment and the process of measurement.