物理学中隐藏的一条数学公理

本文首先介绍了Gdel的不完全性定理和不可判定的概念。其次指出在二阶的标准分析模型M中,普遍存在不可判定的积分公式,如A_6:integral from n=0 to =∞sintdt=1等。第三,本文介绍了物理学Coulomb散射中的通用的数学公式(3,1):integral from ((d~3x/|x|)e~(-iq·x)=4π/|q|~2并证明了A_6和(3,1)的等价性。第四,根据Gdel的不完全性定理和不可判定的概念,本文认为(3,1),或等价地数学公式A_6可以作为物理学中使用的局部的数学公理。

A Mathematical Axiom Hiding In Physics

Ⅰ、The paper introduces the notion of undecidability and incompleteness theorem of Godel. Ⅱ, The paper points out that there are almost everywhere undecidable integral formulae in the second-order model M of standard analysis,for example the fomula . Ⅲ、The paper introduces a mathematical formula(3,1) : ,which is commonly used in the Coulomb settering in physics,and proves that A6is equivalent to(3,1). Ⅳ ,According to Godel's incompleteness theorem and the notion of undecidability,the paper claims that the formula(3,1) ,or equivalently ,the formula A6 may be undertaken to be a local mathematical axiom in physics.