Antisymmetry: Fundamentals and Applications

Abstract

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, or chemical species. 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 described.