标量和矢量数标度的主纤维丛描述：应用于规范理论
Principal fiber bundle description of number scaling for scalars and vectors: Application to gauge theory
摘要：
本文的目的是把数字标度及其对物理和几何的影响的描述放在一个更坚实的基础上，并使其更容易理解。一个主要的观点是，两个不同的概念，数和数值结合在数字结构的通常表示。只要考虑每种数字类型的一个结构，这就是有效的。当考虑每个数字类型的不同结构时，它无效。数结构的基本集合的元素，单独考虑，没有意义。它们作为数结构的元素获得意义或价值。描述了空间流形或时空流形M上的纤维丛。纤维由许多实数或复数结构和向量空间结构的集合组成。结构由实数或复数比例因子s参数化。纤维层的向量空间s具有相同层的实数或复数结构作为标量。描述了在相邻M位置处和相邻缩放级别处将标量和向量空间结构相关的连接。描述了标量和向量结构值域，并得到了这些域的协变导数。出现了两个复向量场，每个复向量场具有一个实域和一个虚域，其中一个复域与$M$中的位置相关联，另一个复域与位置相关的缩放因子相关联。标量场和向量场的协变导数的推导给出相同的向量场。推导表明，与标度光纤能级相关的复矢量场是复标量场的梯度。这些结果在规范理论中的应用表明，与M位置相关的矢量场的虚部的作用类似于电磁场。其他三个领域的物理相关性，如果有的话，是未知的。
英文摘要：
The purpose of this paper is to put the description of number scaling and its effects on physics and geometry on a firmer foundation, and to make it more understandable. A main point is that two different concepts, number and number value are combined in the usual representations of number structures. This is valid as long as just one structure of each number type is being considered. It is not valid when different structures of each number type are being considered. Elements of base sets of number structures, considered by themselves, have no meaning. They acquire meaning or value as elements of a number structure. Fiber bundles over a space or space time manifold, M, are described. The fiber consists of a collection of many real or complex number structures and vector space structures. The structures are parameterized by a real or complex scaling factor, s. A vector space at a fiber level, s, has, as scalars, real or complex number structures at the same level. Connections are described that relate scalar and vector space structures at both neighbor M locations and at neighbor scaling levels. Scalar and vector structure valued fields are described and covariant derivatives of these fields are obtained. Two complex vector fields, each with one real and one imaginary field, appear, with one complex field associated with positions in $M$ and the other with position dependent scaling factors. A derivation of the covariant derivative for scalar and vector valued fields gives the same vector fields. The derivation shows that the complex vector field associated with scaling fiber levels is the gradient of a complex scalar field. Use of these results in gauge theory shows that the imaginary part of the vector field associated with M positions acts like the electromagnetic field. The physical relevance of the other three fields, if any, is not known.
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