Generalized symmetry in crystal physics

• Published in: Computers & mathematics with applications (1987) Vol. 16; no. 5; pp. 407 - 424
• Main Author: Koptsik, V.A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 1988
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/0898-1221(88)90231-3

The external and internal symmetry groups of the matter object and physical processes with a complex structure and the internal degrees of the freedom are combined into single groups of their generalized coloured symmetry by means of the wreath product of these groups. It is shown that the colour symmetry groups of different types are widely used in the tensor and magnetic crystal physics, the crystal structure analysis and in the theory of structure phase transitions for the symmetry description of the structure and physical behaviour of non-rigid molecular crystals, incommensurate crystal phases and icosahedric quasicrystals, etc. Some difficult problems in this field are solved. It is shown that the colour symmetry approach complementary to the irreducible and induced representation of classical symmetry groups expand the whole field of the symmetry analysis of modern physical problems.