论文标题
Feynman的整体路径A Henstock Indever不可或缺：调查和开放问题
The Feynman integral path a Henstock integral: a survey and open problems
论文作者
论文摘要
Feynman路径积分是在所有可能路径的空间上定义的。它一直是开发量子力学的强大工具。 Feynman集成的绝对价值是不可集成的，因此Feynman无法使用Lebesgue集成理论。但是，它正式作为Henstock积分（不需要测量概念）形式存在，并且是通常出现在路径积分中的普通积分的合适替代品。费曼（Feynman）证明了他的理论与量子力学的传统表述的等效性，因为他的路径积分满足了Schrödinger方程。另一方面，Feynman的路径积分与Feynman的图有关。为了在Feynman的图中应用此积分，有必要交换积分$ \ int _ {\ Mathbb {r}^t} $和系列。考虑到Henstock的积分和主导的融合定理的版本，我们讨论了交换积分和总和的不可能。即使是通过使用的几种数学形式主义也没有证明这一点。
The Feynman path integral is defined over the space $\mathbb{R}^T$ of all possible paths; it has been a powerful tool to develop Quantum Mechanics. The absolute value of Feynman's integrand is not integrable, then Lebesgue integration theory could not be used by Feynman. However, it exists formally as a Henstock integral (which does not require the measure concept) and is a suitable alternative to the ordinary integrals that normally appear in path integrals. Feynman proved the equivalence of his theory with the traditional formulation of Quantum Mechanics, since his path integral satisfies Schrödinger's equation. On the other hand, Feynman's path integral is related to the diagrams of Feynman. For the application of this integral in Feynman's diagrams it is necessary to exchange the integral $\int_{\mathbb{R}^T}$ and the series. We discuss the impossibility to exchange the integral and the sum, considering integral of Henstock and the version of Dominated Convergence Theorem. Even it has not been proved through the several mathematical formalisms that have been used.
