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Wedge reversion antisymmetry and 41 types of physical quantities in arbitrary dimensions.
Acta Crystallographica Section A: Foundations and Advances ( IF 1.9 ) Pub Date : 2020-04-28 , DOI: 10.1107/s205327332000217x Venkatraman Gopalan 1
Acta Crystallographica Section A: Foundations and Advances ( IF 1.9 ) Pub Date : 2020-04-28 , DOI: 10.1107/s205327332000217x Venkatraman Gopalan 1
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It is shown that there are 41 types of multivectors representing physical quantities in non-relativistic physics in arbitrary dimensions within the formalism of Clifford algebra. The classification is based on the action of three symmetry operations on a general multivector: spatial inversion, 1, time-reversal, 1', and a third that is introduced here, namely wedge reversion, 1†. It is shown that the traits of `axiality' and `chirality' are not good bases for extending the classification of multivectors into arbitrary dimensions, and that introducing 1† would allow for such a classification. Since physical properties are typically expressed as tensors, and tensors can be expressed as multivectors, this classification also indirectly classifies tensors. Examples of these multivector types from non-relativistic physics are presented.
中文翻译：
楔形回复反对称性和任意尺寸的41种物理量。
结果表明，在克利福德代数的形式主义内，有41种类型的多矢量表示非相对论物理学中任意维度上的物理量。该分类基于三个对称运算对通用多矢量的作用：空间反演1，时间反转1'和此处介绍的第三个对称运算，即楔形反转1†。结果表明，“轴性”和“手性”的特性不是将多向量的分类扩展到任意维度的良好基础，引入1†可以进行这种分类。由于物理属性通常表示为张量，而张量可以表示为多向量，因此此分类也间接地将张量分类。提出了非相对论物理学中这些多向量类型的示例。
更新日期：2020-04-28
中文翻译：
楔形回复反对称性和任意尺寸的41种物理量。
结果表明，在克利福德代数的形式主义内，有41种类型的多矢量表示非相对论物理学中任意维度上的物理量。该分类基于三个对称运算对通用多矢量的作用：空间反演1，时间反转1'和此处介绍的第三个对称运算，即楔形反转1†。结果表明，“轴性”和“手性”的特性不是将多向量的分类扩展到任意维度的良好基础，引入1†可以进行这种分类。由于物理属性通常表示为张量，而张量可以表示为多向量，因此此分类也间接地将张量分类。提出了非相对论物理学中这些多向量类型的示例。
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