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Application of unitary groups for determining tensor components in crystals and selection principles for phase transitions
Author(s) -
Kustov E. F.,
Zakharov N. A.,
Steczko G.
Publication year - 1979
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220910104
Subject(s) - tensor (intrinsic definition) , point group , unitary state , mathematics , series (stratigraphy) , group (periodic table) , interpretation (philosophy) , symmetry (geometry) , pure mathematics , symmetry operation , rotation (mathematics) , combinatorics , physics , geometry , quantum mechanics , computer science , political science , law , paleontology , biology , programming language
The paper is concerned with compound series of unitary groups, of rotation groups and point groups for classification of various tensor components in crystals, which have various components in relation to a rotation group and a permutation group. For this purpose the following series U [γ]γ ⊃ R [γ]γ ⊃ … ⊃ G is being introduced, where γ represents a vector (a pseudovector); then the number of various branches which end with a unit group G determines the number of various tensor components, which have obvious properties for reduction symmetry. When classifying in this way, a new interpretation of selection principles for phase transitions in crystals can be introduced.