Physical applications of crystallographic color groups: Tensor fields in crystals

Abstract

The theory of permutational crystallographic color groups is used to construct tables of the $k=0$ irreducible representations whose basis functions are linear combinations of the components of tensor fields defined on the atoms of an arbitrary crystal. As examples of their use, these tables are shown to be applicable in determining the $k=0$ vibrational and magnetic modes of a crystal, the infrared and Raman-active vibrational modes, in testing the validity of the Jahn-Teller theorem in crystals, and in applying the tensor-field criterion in the Landau theory of continuous phase transitions in crystals.