论文标题
部分可观测时空混沌系统的无模型预测
Local mathematics and scaling field: effects on local physics and on cosmology
论文作者
论文摘要
本文的起源始于杨米尔斯的观察，即在一个位置代表质子的质子的状态并不能确定哪种状态代表另一个位置的iSospin空间中的质子。这是由不同位置向量空间之间的统一量规变换运算符（y，x）$的存在来解释的。该操作员定义了不同位置的向量空间的同一状态概念。如果$ψ$是$ x $的向量空间中的状态，则$ u（y，x）ψ$在vector Space中的状态相同，$ y $。向量空间在其公理描述中包括标量字段。这些作为规范出现，在向量标量乘法等下关闭等。这导致了冲突：局部向量空间和全局标量字段。在这里，通过用本地标量字段替换全局标量字段来消除这种冲突。这些由$ \ bar {s} _ {x} $表示，其中$ x $是Euclidean空间或时空时间的任何位置。这里$ s $代表不同类型的数字（自然，整数，理性，真实和复杂）。标量场与向量空间和杨工厂的观察的关联提出了一个问题，什么与杨工厂对数字的观察相对应？答案是，在数学的通常使用中混合了两个不同的概念，数字和数字含义或价值。这两个概念是不同的。
The origin of this paper starts with the observation by Yang Mills that what state represents a proton in isospin space at one location does not determine what state represents a proton in isospin space at another location. This is accounted for by the presence of a unitary gauge transformation operator, $U(y,x)$, between vector spaces at different locations. This operator defines the notion of same states for vector spaces at different locations. If $ψ$ is a state in a vector space at $x$ then $U(y,x)ψ$ is the same state in the vector space at $y$. Vector spaces include scalar fields in their axiomatic description. These appear as norms, closure under vector scalar multiplication, etc. This leads to a conflict: local vector spaces and global scalar fields. Here this conflict is removed by replacing global scalar fields with local scalar fields. These are represented by $\bar{S}_{x}$ where $x$ is any location in Euclidean space or space time. Here $S$ represents the different type of numbers, (natural, integers, rational, real, and complex). The association of scalar fields with vector spaces and the Yang Mills observation raises the question, What corresponds to the Yang Mills observation for numbers? The answer is that two different concepts, number and number meaning or value, are conflated in the usual use of mathematics. These two concepts are distinct.
