Symmetry is fundamental to understanding our physical world. An antisymmetry operation switches between two different states of a trait, such as two time-states, position-states, charge-states, spin-states, chemical-species etc. This review covers the fundamental concepts of antisymmetry, and focuses on four antisymmetries, namely spatial inversion in point groups, time reversal, distortion reversal and wedge reversion. The distinction between classical and quantum mechanical descriptions of time reversal is presented. Applications of these antisymmetries in crystallography, diffraction, determining the form of property tensors, classifying distortion pathways in transition state theory, finding minimum energy pathways, diffusion, magnetic structures and properties, ferroelectric and multiferroic switching, classifying physical properties in arbitrary dimensions, and antisymmetry-protected topological phenomena are presented.

中文翻译：

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反对称：基础和应用

对称性是理解我们物理世界的基础。反对称操作在特征的两个不同状态之间切换，例如两个时间状态、位置状态、电荷状态、自旋状态、化学物种等。这篇综述涵盖了反对称的基本概念，并着重于四种反对称，即点群空间反演、时间反演、畸变反演和楔形反演。提出了时间反转的经典和量子力学描述之间的区别。这些反对称性在晶体学、衍射、确定性质张量的形式、在过渡态理论中对畸变路径进行分类、寻找最小能量路径、扩散、磁性结构和性质、铁电和多铁性转换中的应用，