New group theoretical methods in physics of imperfect crystals and the theory of structure phase transitions

Abstract

The symmetry theory of imperfect, magnetic or non-rigid crystals with internal degrees of freedom is developed. The theory is based on the abstract symmetry conservation (or extension) law and on the construction of wreath products of two groups which generalise the concept of direct and semidirect product. Elements of the band theory of commensurate and incommensurate crystals are also given.