晶体对称允许物理性质的代数

中文摘要 AI 辅助

由122个磁点群（MPGs）给出的物理系统的对称性，对任何物理张量仅导致21组限制。这些所谓的张量形式由R. R. Birss（《对称性与磁性》，北荷兰出版社，阿姆斯特丹，1964年）用字母A至U标记。本文提出了一个关于性质相关点群（PRPGs）的新概念。研究表明，与21个非中心对称晶体学点群（CPGs）同构的21个PRPGs对应于21种张量形式。因此，可以用PRPGs作为对应于张量形式的数学对象，而不是使用从A到U的符号。根据诺伊曼原理，给定的多极分量仅在描述系统对称性的群是该多极分量对称性的子群时才被允许存在于系统中。每个张量可以用多极自由度来表示，即它对应于由给定PRPG所允许的所有多极分量的一个子集。这些关系导致了张量形式的代数，其中允许的张量分量空间和PRPG算子空间在某种程度上是对偶的。

英文摘要

The symmetry of a physical system given by the 122 magnetic point groups (MPGs) leads to only 21 sets of restrictions on any physical tensors. Those, so called, tenor forms were labeled by letters from A to U by R. R. Birss (Symmetry and Magnetism, North Holland, Amsterdam, 1964). A new concept of property-related point groups (PRPGs) is proposed. It is shown that the 21 PRPGs isomorphic to the 21 non-centrosymmetric crystallographic point groups (CPGs) corresponds to the 21 tensor forms. Therefore instead of a symbols from A to U one can use PRPGs as mathematical objects corresponding to the tenor forms. From the Neumann's principle given multipole component is only allowed in a system when a group describing symmetry of the system is a subgroup of the multipole component symmetry. Each tensor can be expressed in the terms of the multipole degrees of freedom, i.e. it corresponds to a subset of all multipole components allowed by given PRPG. Those relations leads to the algebra of tensor forms, where space of allowed tensor components and space of PRPG operators are somehow dual to each other.

发表机构

• Forschungszentrum Jülich GmbH（于利希研究中心）
• RWTH Aachen University（亚琛工业大学）

机构由 AI 辅助整理，请以论文原文为准。