Antisymmetry: Fundamentals and Applications

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.