物理结构理论的数学基础和结果
The Mathematical Basics and the Results of the Theory of physical structures
摘要：
物理结构理论（TPS）是由余毅中教授提出的。Kulakov是为了对物理定律进行分类。该理论的发展历史在他的专著[1]中给出。一个物理结构是一个几何的一个或两个集的度量函数分配一个数字给每对点。在库拉科夫看来，它的唯象对称性意味着，对于每一个有限数量点的集合，它们的倒易距离都是函数相关的。这样的几何被赋予了一种克莱因意义下的群对称性，这与唯象对称性是等价的，并且它们中的许多几何都有本质的物理解释。这就是为什么它们要被精确地定义，并作为纯粹的数学对象来探索。在这本专着中，我们对待的数学基础的TPS和目前的结果，尝试在分类已经获得了。我们希望，专着将有兴趣的研究工作者和教师，高级和研究生，以及所有那些有兴趣在代数，几何和理论物理谁愿意使用TPS在他们的研究项目或可能要作出贡献的发展，其数学仪器。
英文摘要：
The theory of Physical Structures (TPS) was put forward by Professor Yu.I. Kulakov for the sake of classifying the laws of Physics. The history of the development of that theory is given in his monograph [1]. A physical structure is a geometry of one or two sets whose metric function assigns a number to every pair of points. Its phenomenological symmetry, under Kulakov, means that for every collection of some finite number of points all of their reciprocal distances are functionally related. Such geometries are endowed with a group symmetry under Klein, which is equivalent to the phenomenological symmetry, and many of them have an essential physical interpretation. That is why they are to be defined precisely and explored as purely mathematical objects. In this monograph we treat the mathematical basics of the TPS and present the results of attempts at classification that have been obtained by now. We hope that the monograph will be of interest for research workers and teachers, senior and post graduate students, as well as to all those interested in algebra, geometry and theoretical physics who would like to use the TPS in their research projects or could want to contribute to the development of its mathematical apparatus.
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