论文标题
有限几何形状的物理
Physics in a finite geometry
论文作者
论文摘要
物理学中没有可测量数量可能具有无限值的规定是必不可少的。同时，在数学上，通常将考虑无限程序考虑的可能性通常被视为理所当然。但是，这种可能性不仅与计算上的轻松性背道而驰，而且还导致现代物理学中最严重的问题，机智，计算出的物理量中无限态度的出现。尤其是，在对集合理论的无穷大公理达成共识后 - 在物理学的每个分支中积分的微积分理论基础的骨干 - 一个人不再排除不可定量的经典田地理论的存在，更不用说可纠正的。相比之下，本文表明，否定无穷大的公理会导致物理作用在有限的几何形状中，以确保所有经典的现场理论都是可量化的。
The stipulation that no measurable quantity could have an infinite value is indispensable in physics. At the same time, in mathematics, the possibility of considering an infinite procedure as a whole is usually taken for granted. However, not only does such possibility run counter to computational feasibleness, but it also leads to the most serious problem in modern physics, to wit, the emergence of infinities in calculated physical quantities. Particularly, having agreed on the axiom of infinity for set theory -- the backbone of the theoretical foundations of calculus integrated in every branch of physics -- one could no longer rule out the existence of a classical field theory which is not quantizable, let alone renormalizable. By contrast, the present paper shows that negating the axiom of infinity results in physics acting in a finite geometry where it is ensured that all classical field theories are quantizable.
